55.12 Röksemdafærsla um veldisgröf, hluti 1

5.12.4 Möguleg jafna falls út frá grafi

5.12.4 - Möguleg jafna falls út frá grafi

Lokaverkefni

Skoðaðu gröfin þrjú sem tákna vísisföllin f, g og h.

Graf þriggja vísisvaxtarfalla í hnitakerfi. Föllin g og h skerast við y-ás í sama punkti, en h vex hraðast. Fallið f byrjar neðar á y-ás og vex hægar en hin tvö.

Föllin f og h eru skilgreind með jöfnunum:

f (x) = 10 \cdot 2^{x}

h (x) = 20 \cdot 4^{x}

Hver af eftirfarandi jöfnum gæti skilgreint fallið g? Undirbúðu rökstuðninginn þinn.

g (x) = 20 \cdot {(1,5)}^{x}

g (x) = 20 \cdot {(2,5)}^{x}

g (x) = 10 \cdot {(3,5)}^{x}

g (x) = 20 \cdot {(4,5)}^{x}

Svar:

g (x) = 20 \cdot {(2,5)}^{x}

Útskýrðu rökstuðninginn þinn.

Lausn

Berðu svarið þitt saman:

Graf g hefur sama skurðpunkt við y-ás og graf h, sem er 20. Það vex hraðar en f en hægar en h, svo vaxtarstuðullinn hlýtur að vera stærri en 2 en minni en 4.

2 b4FYRRI KAFLI 5.12.3 Gröf sem tákna vísishnignun NÆSTI KAFLI 5.12.5 ÆfingarrequestAnimationFrame(function(){$RT=performance.now()});Leita í bók... Algebra 1 (IS) Hefjast handa Um þetta námskeið Nemendur byrja hér Flýtibyrjun Notkun Desmos Ítarefni 1.15 Beint hlutfall 1.15.0 Yfirlit kennslustundar 1.15.1 Að leysa hlutföll 1.15.2 Líkanagerð jafna með beinu hlutfalli 1.15.3 Að nota beint hlutfall til að leysa hagnýt verkefni, hluti 1 1.15.4 Að nota beint hlutfall til að leysa hagnýt verkefni, hluti 2 1.15.5 Æfingar 1.15.6 Samantekt kennslustundar 1.5 Jöfnur og gröf þeirra 1.5.0 Yfirlit kennslustundar 1.5.1 Greining á gröfum línulegra jafna 1.5.2 Teikning línulegra falla með tveimur breytum 1.5.3 Að skoða jöfnu með tveimur breytum og graf hennar, hluti 1 1.5.4 Ritun, teikning og lausn línulegrar jöfnu 1.5.5 Að skoða jöfnu með tveimur breytum og graf hennar, hluti 2 1.5.6 Æfingar 1.5.7 Samantekt kennslustundar 1 Línulegar jöfnur 1.3 Ritun jafna til að líkja eftir samböndum, hluti 2 1.3.0 Yfirlit kennslustundar 1.3.1 Að finna tengsl milli 𝑥 og 𝑦 1.3.2 Að lýsa tengslum með orðum og jöfnum 1.3.3 Að greina og tákna tengsl 1.3.4 Að rita jöfnu til að tákna tengsl 1.3.5 Æfingar 1.3.6 Samantekt kennslustundar 1.4 Jöfnur og lausnir þeirra 1.4.0 Yfirlit kennslustundar 1.4.1 Að finna lausn á jöfnu með einni breytu, hluti 1 1.4.2 Að rita jöfnur til að tákna skorður 1.4.3 Að finna lausn á jöfnu með tveimur breytum 1.4.4 Að finna lausn á jöfnu með einni breytu, hluti 2 1.4.5 Æfingar 1.4.6 Samantekt kennslustundar 1.7 Útskýring á skrefum við umritun jafna 1.7.0 Yfirlit kennslustundar 1.7.1 Að ákvarða hvort núll sé lausn 1.7.2 Að útskýra leyfilegar aðgerðir til að leysa jöfnu 1.7.3 Að skilja jöfnur með enga lausn eða óendanlega margar lausnir 1.7.4 Að leysa jöfnur með deilingu 1.7.5 Æfingar 1.7.6 Samantekt kennslustundar 1.9 Val á réttri breytu til að leysa fyrir, hluti 2 1.9.0 Yfirlit kennslustundar 1.9.1 Að umrita jöfnu með þremur breytum 1.9.2 Að skrifa jöfnu til að tákna skorðu 1.9.3 Að skrifa og umrita jöfnur með tveimur breytum 1.9.4 Að leysa fyrir tiltekna breytu 1.9.5 Æfingar 1.9.6 Samantekt kennslustundar 1.10 Tenging jafna við gröf, hluti 1 1.10.0 Yfirlit kennslustundar 1.10.1 Að túlka jöfnur í samhengi 1.10.2 Að teikna gröf jafna í samhengi 1.10.3 Að skrifa jöfnur á staðalformi og teikna gröf þeirra 1.10.4 Að para saman jöfnur og gröf 1.10.5 Æfingar 1.10.6 Samantekt kennslustundar 1.11 Tenging jafna við gröf, hluti 2 1.11.0 Yfirlit kennslustundar 1.11.1 Að beita dreifireglu til að umrita stæður 1.11.2 Að tengja jöfnur með tveimur breytum, gröf þeirra og aðstæður 1.11.3 Að beita táknrænni og óhlutbundinni röksemdafærslu um línulegar jöfnur 1.11.4 Að bera kennsl á eiginleika grafs 1.11.5 Æfingar 1.11.6 Samantekt kennslustundar 1.12 Ritun jöfnu línu 1.12.0 Yfirlit kennslustundar 1.12.1 Að nota formúlu fyrir hallatölu 1.12.2 Að skrifa jöfnu út frá hallatölu og skurðpunkti við y-ás 1.12.3 Að skrifa jöfnu út frá hallatölu og punkti 1.12.4 Að skrifa jöfnur á mismunandi formum 1.12.5 Að skrifa jöfnu út frá tveimur punktum 1.12.6 Að velja aðferð til að skrifa jöfnu 1.12.7 Æfingar 1.12.8 Samantekt kennslustundar 1.13 Línur út frá töflum og gröfum 1.13.0 Yfirlit kennslustundar 1.13.1 Að skrifa línulegar jöfnur 1.13.2 Að búa til töflur út frá lýsingum með orðum 1.13.3 Að para saman töflur, jöfnur og gröf 1.13.4 Að búa til töflu út frá jöfnu 1.13.5 Æfingar 1.13.6 Samantekt kennslustundar 1. hluti: Samantekt 1.8 Val á réttri breytu til að leysa fyrir, hluti 1 1.8.0 Yfirlit kennslustundar 1.8.1 Að lýsa tengslum milli tveggja stærða 1.8.2 Að velja gagnlegasta form jöfnu 1.8.3 Að skrifa jöfnur og einangra breytur 1.8.4 Að skrifa jöfnur út frá málum forma 1.8.5 Æfingar 1.8.6 Samantekt kennslustundar 1.1 Könnun á stæðum og jöfnum 1.1.0 Yfirlit kennslustundar 1.1.1 Skilningur á gildi 1.1.2 Búa til stæður til að áætla kostnað, hluti 1 1.1.3 Skilningur á skorðum 1.1.4 Búa til stæður til að áætla kostnað, hluti 2 1.1.5 Æfing 1.1.6 Samantekt kennslustundar 1.2 Ritun jafna til að líkja eftir samböndum, hluti 1 1.2.0 Yfirlit kennslustundar 1.2.1 Að finna prósentu af 200 1.2.2 Líkanagerð með jöfnum til að finna brúnir platónskra margflötunga 1.2.3 Ritun jafna til að tákna tengsl 1.2.4 Ritun jafna til að tákna tengsl með prósentum 1.2.5 Að rita jöfnur fyrir stuttermabolapöntun 1.2.6 Æfingar 1.2.7 Samantekt kennslustundar Kafli 1 Yfirlit og undirbúningur Yfirlit yfir 1. hluta Stutt upprifjun: að leysa línulegar jöfnur Stutt upprifjun: að flokka jöfnur Finna hnit: Smákennsla upprifjun Yfirlit yfir 1. hluta: samantekt Stuðningur við alla nemendur Undirbúningur fyrir árangur Námsráð Að skapa þitt besta sjálf Að byggja upp tengsl 1.14 Ritun jafna fyrir samsíða og hornréttar línur 1.14.0 Yfirlit kennslustundar 1.14.1 Notkun punkthallaforms til að rita jöfnu línu 1.14.2 Ritun jafna á punkthallaformi og hallatöluformi 1.14.3 Að skrifa jöfnu línu sem er samsíða gefinni línu 1.14.4 Að skrifa jöfnu línu sem er hornrétt á gefna línu 1.14.5 Að skrifa jöfnu línu sem er samsíða eða hornrétt á ás 1.14.6 Að teikna samsíða og hornréttar línur 1.14.7 Æfingar 1.14.8 Samantekt kennslustundar 1.6 Jafngildar jöfnur 1.6.0 Yfirlit kennslustundar 1.6.1 Að kanna jafngildar stæður 1.6.2 Að setja tengsl fram sem jöfnur 1.6.3 Könnun á skyldum jöfnum 1.6.4 Að bera kennsl á skyldar jöfnur 1.6.5 Æfingar 1.6.6 Samantekt kennslustundar Verkefni 1: Hallatölur og skurðpunktar Verkefni 1 Yfirlit Taka eftir og velta fyrir sér: einkenni grafs Pörun grafa og jafna 2.14 Lausnir á línulegum ójöfnuhneppum með tveimur breytistærðum 2.14.0 Yfirlit kennslustundar 2.14.1 Að setja upp jöfnur til að leysa gátu 2.14.2 Að finna tvennd gilda sem uppfyllir margar ójöfnur 2.14.3 Að skrifa ójöfnuhneppi sem tákna aðstæður 2.14.4 Að teikna lausnamengi ójöfnuhneppa 2.14.5 Að skrifa ójöfnur fyrir aðstæður og sýna þær á grafi 2.14.6 Æfingar 2.14.7 Samantekt kennslustundar 2 Línulegar ójöfnur og jöfnuhneppi 2.1 Ritun og teikning jöfnuhneppa 2.1.0 Yfirlit kennslustundar 2.1.1 Að skilja skorður og gildi 2.1.2 Að skrifa og teikna jöfnur 2.1.3 Að uppfylla skorður 2.1.4 Að kanna jöfnuhneppi 2.1.5 Æfingar 2.1.6 Samantekt kennslustundar 2.2 Ritun jöfnuhneppa 2.2.0 Yfirlit kennslustundar 2.2.1 Túlkun á gröfum jöfnuhneppa 2.2.2 Að skrifa jöfnuhneppi út frá töflum 2.2.3 Gröf jöfnuhneppa 2.2.4 Jöfnuhneppi í raunverulegum aðstæðum 2.2.5 Æfingar 2.2.6 Samantekt kennslustundar 2.5 Lausn jöfnuhneppa með eyðingu, 2. hluti 2.5.0 Yfirlit kennslustundar 2.5.1 Að skrifa og prófa nýjar jöfnur 2.5.2 Að leggja saman tvær jöfnur í jöfnuhneppi 2.5.3 Að leysa línuleg jöfnuhneppi með tveimur breytum 2.5.4 Að leysa jöfnuhneppi með raunverulegum dæmum 2.5.5 Æfingar 2.5.6 Samantekt kennslustundar 2.6 Lausn jöfnuhneppa með eyðingu, 3. hluti 2.6.0 Yfirlit kennslustundar 2.6.1 Að margfalda jöfnur með tölu 2.6.2 Að skrifa nýtt jöfnuhneppi til að leysa gefið jöfnuhneppi 2.6.3 Að finna lausnir í óröðuðum söfnum jafngildra jöfnuhneppa 2.6.4 Að búa til jafngild jöfnuhneppi 2.6.5 Æfingar 2.6.6 Samantekt kennslustundar 2.7 Línuleg jöfnuhneppi og lausnir þeirra 2.7.0 Yfirlit kennslustundar 2.7.1 Línuleg jöfnuhneppi með óendanlega mörgum lausnum 2.7.2 Línuleg jöfnuhneppi sem hafa enga lausn 2.7.3 Að flokka jöfnuhneppi eftir fjölda lausna 2.7.4 Að skrifa samkvæm og ósamkvæm jöfnuhneppi 2.7.5 Æfingar 2.7.6 Samantekt kennslustundar 2.8 Framsetning aðstæðna með ójöfnum 2.8.0 Yfirlit kennslustundar 2.8.1 Að skilja ójöfnutákn 2.8.2 Að greina skorður í ójöfnum 2.8.3 Að skrifa ójöfnur sem tákna skorður 2.8.4 Að skrifa fleiri ójöfnur 2.8.5 Æfingar 2.8.6 Samantekt kennslustundar 2.9 Lausnir ójafna 2.9.0 Yfirlit kennslustundar 2.9.1 Að skrá lausnir ójafna 2.9.2 Að sýna lausnir ójafna á talnalínu 2.9.3 Að skilja merkingu ójöfnu 2.9.4 Að átta sig á ójöfnum og lausnum þeirra 2.9.5 Að bera saman jöfnur og ójöfnur 2.9.6 Að nota tækni til að skoða lausnir ójafna myndrænt 2.9.7 Að finna lausnir ójafna á talnalínu 2.9.8 Æfingar 2.9.9 Samantekt kennslustundar 2.10 Ritun og lausn ójafna með einni breytistærð 2.10.0 Yfirlit kennslustundar 2.10.1 Að skrifa ójöfnu sem táknar skorðu 2.10.2 Að nota ójöfnur til að leysa verkefni 2.10.3 Mismunandi leiðir til að leysa ójöfnu 2.10.4 Að para saman ójöfnur og lausnir 2.10.5 Að leysa ójöfnur 2.10.6 Að skrifa ójöfnur sem tákna aðstæður 2.10.7 Æfingar 2.10.8 Samantekt kennslustundar 2.11 Teikning línulegra ójafna með tveimur breytistærðum 2.11.0 Yfirlit kennslustundar 2.11.1 Að nota útreikninga og röksemdafærslu 2.11.2 Að finna lausnir ójafna í hnitakerfi 2.11.3 Að teikna lausnamengi ójafna 2.11.4 Að skyggja svæði við markalínu 2.11.5 Æfingar 2.11.6 Samantekt kennslustundar 2.12 Notkun línulegra ójafna sem skorður 2.12.0 Yfirlit kennslustundar 2.12.1 Að teikna graf sem táknar jöfnu 2.12.2 Að skrifa ójöfnu sem táknar skorðu 2.12.3 Að teikna lausnamengi og túlka punkta 2.12.4 Að greina punkta á markalínu 2.12.5 Að ákvarða hvort punktar séu lausnir ójöfnu 2.12.6 Æfingar 2.12.7 Samantekt kennslustundar 2.13 Lausn vandamála með ójöfnum með tveimur breytistærðum 2.13.0 Yfirlit kennslustundar 2.13.1 Að teikna lausnamengi ójafna með grafreiknitæki 2.13.2 Að leysa verkefni með ójöfnum með tveimur breytum 2.13.3 Að para saman framsetningar ójafna 2.13.4 Að leysa verkefni með ójöfnum með töflum 2.13.5 Að teikna lausnamengi ójöfnu 2.13.6 Æfingar 2.13.7 Samantekt kennslustundar Verkefni 2: Líkanagerð með ójöfnuhneppum með tveimur breytistærðum Yfirlit verkefnis 2 Að ákvarða lausn ójafna Að túlka safn stærðfræðilíkana Að vinna stærðfræðilega líkanagerð Samantekt 2. hluta 2. hluti Yfirlit og undirbúningur 2. hluti Yfirlit Að ákvarða röðuðu tvenndina: upprifjun smákennslu Að finna hallatölu og skurðpunkt við y-ás: upprifjun smákennslu Að finna skurðpunkta við x-ás og y-ás: upprifjun smákennslu 2. hluti: Samantekt á yfirliti 2.3 Lausn jöfnuhneppa með innsetningu 2.3.0 Yfirlit kennslustundar 2.3.1 Að finna tengsl milli grafa og jafna 2.3.2 Að athuga lausnir jöfnuhneppa 2.3.3 Að leysa jöfnur með innsetningaraðferðinni 2.3.4 Að leysa fleiri jöfnur 2.3.5 Æfingar 2.3.6 Samantekt kennslustundar 2.4 Lausn jöfnuhneppa með eyðingu, 1. hluti 2.4.0 Yfirlit kennslustundar 2.4.1 Að sameina tvær sannar jöfnur 2.4.2 Að leggja saman jöfnur 2.4.3 Að leggja saman og draga frá jöfnuhneppi og nota gröf þeirra 2.4.4 Að velja bestu aðferðina til að leysa jöfnuhneppi 2.4.5 Æfingar 2.4.6 Samantekt kennslustundar 2.15 Lausn vandamála með línulegum ójöfnuhneppum með tveimur breytistærðum 2.15.0 Yfirlit kennslustundar 2.15.1 Að greina gröf sem tákna línulegar jöfnur og ójöfnur 2.15.2 Að ákvarða hvort punktar á markalínum séu lausnir hneppis 2.15.3 Að leysa verkefni með mörgum skorðum samtímis 2.15.4 Að finna hvaða svæði grafs tilheyra lausn hneppis 2.15.5 Æfingar 2.15.6 Samantekt kennslustundar Verkefni 3: Tölfræði tveggja breyta Yfirlit yfir verkefni 3 Að áætla lengdir Að greina gögn 3 Tölfræði tveggja breytistærða 3. hluti Yfirlit og undirbúningur Yfirlit 3. hluta Að greina mynstur: Upprifjun smákennslu Að greina jákvæða og neikvæða leitni: Upprifjun smákennslu Að túlka hallatölu og skurðpunkt við y-ás: Upprifjun smákennslu Samantekt yfirlits 3. hluta 3.2 Bestunarlínur 3.2.0 Yfirlit kennslustundar 3.2.1 Að velja bestu línuna 3.2.2 Að finna línu sem fellur best að gögnunum 3.2.3 Að skrifa línuleg líkön án tæknibúnaðar 3.2.4 Að meta hversu vel línulegt líkan fellur að gögnum 3.2.5 Að vinna með línur sem falla að gögnum 3.2.6 Æfingar 3.2.7 Samantekt kennslustundar 3.3 Leifar 3.3.0 Yfirlit kennslustundar 3.3.1 Að draga áætlað gildi frá raungildi 3.3.2 Að teikna og greina leifar 3.3.3 Að para saman leifarit og dreifirit 3.3.4 Að finna línu sem fellur best að gögnum út frá leifariti 3.3.5 Æfingar 3.3.6 Samantekt kennslustundar 3.4 Fylgnistuðullinn 3.4.0 Yfirlit kennslustundar 3.4.1 Að bera saman dreifirit með línulegri og ólínulegri leitni 3.4.2 Greining mismunar á punktaritum 3.4.3 Að finna fylgnistuðul með tæknibúnaði 3.4.4 Pörun fylgnistuðla 3.4.5 Að nota fylgnistuðul til að meta línu sem fellur að gögnum 3.4.6 Æfing 3.4.7 Samantekt kennslustundar 3.5 Notkun fylgnistuðulsins 3.5.0 Yfirlit kennslustundar 3.5.1 Að nota tvíbreytugögn í samhengi 3.5.2 Að finna og nota fylgnistuðul til að túlka styrk línulegs sambands 3.5.3 Að nota fylgnistuðul til að lýsa sambandi tveggja breyta 3.5.4 Að túlka fylgnistuðul 3.5.5 Æfingar 3.5.6 Samantekt kennslustundar 3.6 Orsakasambönd 3.6.0 Yfirlit kennslustundar 3.6.1 Að lýsa sambandi milli breyta 3.6.2 Að lýsa hvernig tvær breytur tengjast 3.6.3 Að nota hugtakið orsakasamband 3.6.4 Að ákvarða tegund sambands 3.6.5 Æfingar 3.6.6 Samantekt kennslustundar Lokaorð 3. hluta 3.1 Línuleg líkön 3.1.0 Yfirlit kennslustundar 3.1.1 Að kanna dreifirit 3.1.2 Að búa til dreifirit út frá gögnum 3.1.3 Að túlka hallatölu og skurðpunkt við y-ás í línulegu líkani 3.1.4 Að túlka hallatölu og skurðpunkt við y-ás í dreifiriti 3.1.5 Að nota jöfnu línu sem fellur vel að gögnum 3.1.6 Æfingar 3.1.7 Samantekt kennslustundar 4 Föll Rannsóknarverkefni: Skilgreining falla Yfirlit yfir rannsóknarverkefni Hermun sambanda Hvað er fall? Mismunandi tegundir falla Yfirlit og undirbúningur fyrir 4. hluta Yfirlit 4. hluta Finna hallatölu: Upprifjun Lýsa gröfum: Upprifjun Framlengja mynstur: Upprifjun Yfirlit 4. hluta: Lokaorð 4.1 Lýsing og teikning aðstæðna 4.1.0 Yfirlit kennslustundar 4.1.1 Samanburður tveggja sambanda með röksemdafærslu 4.1.2 Myndræn röksemdafærsla um samband tveggja stærða 4.1.3 Skoðun vensla og falla 4.1.4 Lýsing á fallssamböndum 4.1.5 Að setja tengsl tveggja breyta fram með líkani 4.1.6 Æfing 4.1.7 Samantekt kennslustundar 4.2 Ritháttur falla 4.2.0 Yfirlit kennslustundar 4.2.1 Að túlka gröf til að svara spurningum 4.2.2 Túlkun fullyrðinga á rithætti falla 4.2.3 Að finna nákvæmlega eitt úttak fyrir hvert inntak 4.2.4 Að skilja falltáknun með hagnýtum verkefnum 4.2.5 Æfingar 4.2.6 Samantekt kennslustundar 4.3 Túlkun með rithætti falla 4.3.0 Yfirlit kennslustundar 4.3.1 Að bera saman fallgildi 4.3.2 Að rita staðhæfingar út frá falltáknun 4.3.3 Að bera saman staðhæfingar í falltáknun 4.3.4 Að nota falltáknun í raunverulegu dæmi 4.3.5 Æfingar 4.3.6 Samantekt kennslustundar 4.4 Notkun ritháttar falla til að lýsa reglum, hluti 1 4.4.0 Yfirlit kennslustundar 4.4.1 Að nota falltáknun í gildistöflum 4.4.2 Að skilgreina föll með reglu 4.4.3 Að nota töflur til að finna fallreglur 4.4.4 Að rita reglu með falltáknun 4.4.5 Æfingar 4.4.6 Samantekt kennslustundar 4.6 Eiginleikar grafa 4.6.0 Yfirlit kennslustundar 4.6.1 Að túlka staðhæfingar í falltáknun 4.6.2 Að greina gröf falla 4.6.3 Að tengja saman graf og orðalýsingu á falli 4.6.4 Helstu eiginleikar línulegra falla 4.6.5 Að túlka gröf 4.6.6 Æfingar 4.6.7 Samantekt kennslustundar 4.7 Hallatala fundin 4.7.0 Yfirlit kennslustundar 4.7.1 Að reikna gildi brota 4.7.2 Að finna hallatölu út frá töflum, gröfum og punktum 4.7.3 Að rita línulegar jöfnur 4.7.4 Að rita jöfnur út frá tveimur punktum 4.7.5 Æfingar 4.7.6 Samantekt kennslustundar 4.8 Notkun grafa til að finna meðalbreytingarhraða 4.8.0 Yfirlit kennslustundar 4.8.1 Að bera saman breytingar á úttaki út frá inntaki 4.8.2 Meðalbreytingarhraði og hallatala 4.8.3 Meðalbreytingarhraði fundinn og túlkaður 4.8.4 Breytingarhraði línulegra falla 4.8.5 Að túlka meðalbreytingarhraða með dæmum úr raunveruleikanum 4.8.6 Æfingar 4.8.7 Samantekt kennslustundar 4.9 Túlkun og gerð grafa 4.9.0 Yfirlit kennslustundar 4.9.1 Að greina og bera saman eiginleika grafa 4.9.2 Að túlka gröf án mælieininga 4.9.3 Að teikna drög að gröfum falla 4.9.4 Framsetning stærða í tilteknum aðstæðum 4.9.5 Að nota orðalýsingar til að búa til gröf falla 4.9.6 Æfingar 4.9.7 Samantekt kennslustundar 4.10 Samanburður grafa 4.10.0 Yfirlit kennslustundar 4.10.1 Að greina gröf og staðhæfingar í falltáknun 4.10.2 Að túlka gröf og staðhæfingar út frá aðstæðum 4.10.3 Samanburður falla sem sett eru fram á aðskildum gröfum 4.10.4 Að bera saman gröf og staðhæfingar sem tákna föll án samhengis 4.10.5 Að greina föll í raunverulegu samhengi 4.10.6 Æfingar 4.10.7 Samantekt kennslustundar 4.11 Teikning falls með umbreytingum 4.11.0 Yfirlit kennslustundar 4.11.1 Að teikna gröf línulegra falla 4.11.2 Lóðréttar hliðranir 4.11.3 Láréttar hliðranir 4.11.4 Lóðréttar teygjur og samþjöppun 4.11.5 Láréttar teygjur og samþjöppun 4.11.6 Að teikna gröf með umbreytingum 4.11.7 Æfingar 4.11.8 Samantekt kennslustundar 4.12 Formengi og myndmengi, hluti 1 4.12.0 Yfirlit kennslustundar 4.12.1 Að ákvarða skynsamleg inntaks- og úttaksgildi 4.12.2 Formengi: inntak falls 4.12.3 Myndmengi: úttak falls 4.12.4 Notkun grafa til að ákvarða formengi falls 4.12.5 Að nota föll til að svara spurningum úr raunveruleikanum 4.12.6 Æfingar 4.12.7 Samantekt kennslustundar 4.13 Formengi og myndmengi, hluti 2 4.13.0 Yfirlit kennslustundar 4.13.1 Mismunandi eiginleikar grafs 4.13.2 Gröf falla 4.13.3 Að finna formengi og myndmengi út frá grafi 4.13.4 Formengi og myndmengi í raunveruleikanum 4.13.5 Graf falls og tengsl formengis og myndmengis 4.13.6 Æfingar 4.13.7 Samantekt kennslustundar 4.14 Runur 4.14.0 Yfirlit kennslustundar 4.14.1 Lýstu mynstrinu 4.14.2 Hvað er runa? 4.14.3 Tengslin milli runa og liða 4.14.4 Reglur fyrir runu 4.14.5 Æfingar 4.14.6 Samantekt kennslustundar 4.15 Kynning á kvótarunum 4.15.0 Yfirlit kennslustundar 4.15.1 Hver eru mynstrin? 4.15.2 Notkun taflna og grafa til að setja fram kvótarunur 4.15.3 Ljúktu við rununa 4.15.4 Tengsl kvótans og liðar í runu 4.15.5 Æfingar 4.15.6 Samantekt kennslustundar 4.16 Kynning á jafnmismunarunum 4.16.0 Yfirlit kennslustundar 4.16.1 Að túlka falltáknun 4.16.2 Hvað er jafnmunaruna? 4.16.3 Runa er tegund falls 4.16.4 Að þekkja og mynda runur 4.16.5 Æfingar 4.16.6 Samantekt kennslustundar 4.17 Framsetning runa 4.17.0 Yfirlit kennslustundar 4.17.1 Að skilgreina runu 4.17.2 Hvað er rakningarregla? 4.17.3 Leiðir til að setja fram runu 4.17.4 Rakningarreglur fyrir kvótarunur 4.17.5 Æfingar 4.17.6 Samantekt kennslustundar 4.18 n-ti liður runu 4.18.0 Yfirlit kennslustundar 4.18.1 Endurteknar aðgerðir 4.18.2 Að greina formengi falls 4.18.3 Skilgreina jafnmunarunu með n-ta liðnum 4.18.4 Skilgreina kvótarunu með n-ta liðnum 4.18.5 Að skipta á milli formúla 4.18.6 Mismunandi tegundir jafna 4.18.7 Æfingar 4.18.8 Samantekt kennslustundar Verkefni 4: Notkun falla til að líkja eftir rafhlöðuorku Yfirlit verkefnis 4 Áætla hleðslutíma rafhlöðu Greina hleðsluprósentu yfir tíma Skrifa jöfnu til að gera líkan af gögnum Samantekt 4. hluta 4.5 Notkun ritháttar falla til að lýsa reglum, hluti 2 4.5.0 Yfirlit kennslustundar 4.5.1 Að finna lausnir jafna 4.5.2 Að nota lóðrétta línuprófið 4.5.3 Samanburður falla 4.5.4 Að nota falltáknun og grafreiknivél 4.5.5 Að finna óþekktar stærðir í línulegum föllum með myndrænni og algebrulegri aðferð 4.5.6 Æfingar 4.5.7 Samantekt kennslustundar 5.7 Greining grafa 5.7.0 Yfirlit kennslustundar 5.7.1 Mynstur í rauntölum 5.7.2 Að bera saman gröf 5.7.3 Að lýsa gröfum 5.7.4 Stærðir sem breytast samkvæmt vísisfalli 5.7.5 Æfingar 5.7.6 Samantekt kennslustundar 5 Kynning á veldisföllum Yfirlit og undirbúningur fyrir 5. hluta Yfirlit 5. hluta Ritun línulegra falla út frá grafi: Upprifjun Túlkun línulegra falla: Upprifjun Reikna gildi veldisstæðna: Upprifjun Yfirlit 5. hluta: Samantekt 5.1 Veldisreglur 5.1.0 Yfirlit kennslustundar 5.1.1 Skilningur á veldum 5.1.2 Notkun margfeldis- og kvótareglna fyrir veldi 5.1.3 Notkun núllveldisreglu og neikvæðra velda 5.1.4 Veldisreglur fyrir veldi 5.1.5 Einföldun velda 5.1.6 Æfingar 5.1.7 Samantekt kennslustundar 5.2 Ræð veldi 5.2.0 Yfirlit kennslustundar 5.2.1 Ferningstölur rifjaðar upp 5.2.2 n-ta rótin 5.2.3 Rótarstæður og ræðir veldisvísar 5.2.4 Veldisreglur með ræðum veldisvísum 5.2.5 Æfingar 5.2.6 Samantekt kennslustundar 5.3 Vaxtarmynstur 5.3.0 Yfirlit kennslustundar 5.3.1 Myndræn framsetning á veldisvexti 5.3.2 Könnun á mismunandi vaxtarmynstrum 5.3.3 Samanburður á tveimur mynstrum 5.3.4 Að tengja stæður og töflur við aðstæður 5.3.5 Að lýsa breytingum á vexti stærðfræðilega 5.3.6 Æfingar 5.3.7 Samantekt kennslustundar 5.4 Framsetning á veldisvexti 5.4.0 Yfirlit kennslustundar 5.4.1 Veldisreglur 5.4.2 Núllveldisreglan 5.4.3 Veldisbreyting: vaxtarstuðullinn 5.4.4 Að teikna gröf veldisstæðna 5.4.5 Að túlka vaxtarstuðul jöfnu 5.4.6 Æfingar 5.4.7 Samantekt kennslustundar 5.5 Framsetning á veldishrörnun 5.5.0 Yfirlit kennslustundar 5.5.1 Að bera kennsl á línulegar stærðir og stærðir sem breytast veldislega 5.5.2 Vísishnignun 5.5.3 Að nota gröf til að sýna vísishnignun 5.5.4 Að rökstyðja veldislíkön 5.5.5 Að skrifa jöfnur sem lýsa vísishnignun 5.5.6 Æfingar 5.5.7 Samantekt kennslustundar 5.6 Neikvæð veldi og staðalform 5.6.0 Yfirlit kennslustundar 5.6.1 Athugun á veldisreglum 5.6.2 Að túlka neikvæða veldisvísa í veldisvexti 5.6.3 Að túlka neikvæða veldisvísa í vísishnignun 5.6.4 Staðalform 5.6.5 Að nota staðalform 5.6.6 Að túlka neikvæða veldisvísa og staðalform 5.6.7 Æfingar 5.6.8 Samantekt kennslustundar 5.8 Veldisaðstæður sem föll 5.8.0 Yfirlit kennslustundar 5.8.1 Merking falls sem sett er fram myndrænt 5.8.2 Framsetning falls sem gildistafla, graf og jafna 5.8.3 Mál falla og falltáknun 5.8.4 Falltáknun 5.8.5 Æfingar 5.8.6 Samantekt kennslustundar 5.9 Túlkun veldisfalla 5.9.0 Yfirlit kennslustundar 5.9.1 Reikna gildi stæðna fyrir mismunandi gildi á x 5.9.2 Greina undirliggjandi tengsl í grafi falls 5.9.3 Teikna gröf jafna til að leysa verkefni 5.9.4 Að velja grafglugga 5.9.5 Túlka gröf til að finna nálguð gildi 5.9.6 Æfingar 5.9.7 Samantekt kennslustundar 5.10 Skoðun á breytingarhraða 5.10.0 Yfirlit kennslustundar 5.10.1 Reikna meðalbreytingarhraða út frá tveimur punktum 5.10.2 Kanna meðalbreytingarhraða í veldisvexti 5.10.3 Kanna meðalbreytingarhraða í vísishnignun 5.10.4 Meðalbreytingarhraði 5.10.5 Æfingar 5.10.6 Samantekt kennslustundar 5.11 Líkanagerð fyrir veldishegðun 5.11.0 Yfirlit kennslustundar 5.11.1 Að breyta grafglugga 5.11.2 Velja viðeigandi líkan 5.11.3 Líkanagerð með vísisföllum 5.11.4 Skoða vísishnignun í samhengi 5.11.5 Nota líkön af tengslum til að svara spurningum 5.11.6 Æfingar 5.11.7 Samantekt kennslustundar 5.12 Röksemdafærsla um veldisgröf, hluti 1 5.12.0 Yfirlit kennslustundar 5.12.1 Líkanagerð með vísishnignun 5.12.2 Jöfnur og gröf þeirra 5.12.3 Gröf sem tákna vísishnignun 5.12.4 Möguleg jafna falls út frá grafi 5.12.5 Æfingar 5.12.6 Samantekt kennslustundar 5.13 Röksemdafærsla um veldisgröf, hluti 2 5.13.0 Yfirlit kennslustundar 5.13.1 Samanburður falla 5.13.2 Að búa til vísisföll út frá gröfum 5.13.3 Samanburður vísisfalla 5.13.4 Að túlka eiginleika grafs vísisfalls 5.13.5 Æfingar 5.13.6 Samantekt kennslustundar 5.14 Hvor breytist hraðar? 5.14.0 Yfirlit kennslustundar 5.14.1 Að greina línulegan vöxt frá veldisvexti 5.14.2 Að nota töflur til að bera saman línuleg föll og vísisföll 5.14.3 Samanburður línulegra falla og vísisfalla 5.14.4 Að nota falltáknun til að bera saman línuleg föll og vísisföll 5.14.5 Æfingar 5.14.6 Samantekt kennslustundar 5.15 Breytingar yfir jöfn bil 5.15.0 Yfirlit kennslustundar 5.15.1 Að rita jafngildar stæður 5.15.2 Fastur breytingarhraði línulegs falls 5.15.3 Vaxtarhraði vísisfalls 5.15.4 Samanburður á línulegum vexti og veldisvexti 5.15.5 Æfingar 5.15.6 Samantekt kennslustundar Verkefni 5: Kynning á veldisföllum Yfirlit verkefnis 5 Greining gagna Að rita jöfnur fyrir mannfjöldalíkön Opin líkanagerð með gagnarannsókn Samantekt á kafla 5 6 Vinna með margliður Yfirlit og undirbúningur fyrir kafla 6 Yfirlit kafla 6 Einföldun stæðna með reglum um veldi: Upprifjun Einföldun stæðna með dreifireglunni: Upprifjun Að finna stærsta samdeili: Upprifjun Yfirlit kafla 6: Samantekt Rannsóknarverkefni kafla 6: Margföldun með flatarmálslíkani Yfirlit rannsóknarverkefnis Að uppgötva flatarmálslíkan Að skilja flatarmálslíkan Að nota flatarmálslíkan Að beita flatarmálslíkani á margliður 6.1 Samlagning og frádráttur margliða 6.1.0 Yfirlit kennslustundar 6.1.1 Að skilja margliður 6.1.2 Að leggja saman og draga frá margliður 6.1.3 Að reikna gildi margliðufalls fyrir gefið gildi 6.1.4 Að leggja saman og draga frá margliðuföll 6.1.5 Upprifjun á samlagningu og frádrætti margliða 6.1.6 Æfingar 6.1.7 Samantekt kennslustundar 6.2 Margföldun margliða 6.2.0 Yfirlit kennslustundar 6.2.1 Margföldun einliða 6.2.2 Margföldun tvíliða 6.2.3 Margföldun margliðu með margliðu 6.2.4 Margföldun sérstakra margfelda 6.2.5 Margföldun margliðufalla 6.2.6 Æfingar 6.2.7 Samantekt kennslustundar 6.3 Deiling margliða 6.3.0 Yfirlit kennslustundar 6.3.1 Deiling með einliðum 6.3.2 Deiling margliða með langdeilingu 6.3.3 Deiling margliða með reikniriti Horners 6.3.4 Deiling margliðufalla og afgangssetningin 6.3.5 Að nota þáttasetninguna 6.3.6 Æfingar 6.3.7 Samantekt kennslustundar 6.4 Stærsti samdeilir og þáttun með hópun 6.4.0 Yfirlit kennslustundar 6.4.1 Að finna þætti 6.4.2 Að finna stærsta samdeili tveggja eða fleiri stæðna 6.4.3 Að taka stærsta samdeili út fyrir sviga í margliðum 6.4.4 Að þátta margliður með hópun 6.4.5 Er hægt að þátta margliðuna? 6.4.6 Æfingar 6.4.7 Samantekt kennslustundar 6.5 Þáttun þríliða 6.5.0 Yfirlit kennslustundar 6.5.1 Að snúa FOIL-aðferðinni við 6.5.2 Þáttun þríliða þar sem forystustuðullinn er 1 6.5.3 Þáttun þríliða með því að prófa sig áfram 6.5.4 Þáttun þríliða með ac-aðferðinni og innsetningu 6.5.5 Að velja eigin aðferð til að þátta þríliði 6.5.6 Æfingar 6.5.7 Samantekt kennslustundar 6.6 Þáttun sérstakra margfelda 6.6.0 Yfirlit kennslustundar 6.6.1 Að bera kennsl á þríliði sem eru ferningar tvíliða 6.6.2 Þáttun þríliða sem eru ferningar tvíliða 6.6.3 Þáttun mismunar tveggja ferninga 6.6.4 Að flokka margliður eftir þáttunaraðferðum 6.6.5 Æfingar 6.6.6 Samantekt kennslustundar 6.7 Almennar aðferðir við þáttun margliða 6.7.0 Yfirlit kennslustundar 6.7.1 Þáttunaraðferðir fyrir margliður 6.7.2 Upprifjun á almennum aðferðum við þáttun margliðu 6.7.3 Beiting almennra aðferða við þáttun 6.7.4 Er margliðan fullþáttuð? 6.7.5 Æfingar 6.7.6 Samantekt kennslustundar Verkefni 6: Margliður og rétthyrningar Yfirlit verkefnis 6 Flatarmál rétthyrninga Mál og flatarmál rétthyrninga Búðu til þína eigin rétthyrninga Samantekt á kafla 6 7 Kynning á annars stigs föllum Yfirlit og undirbúningur fyrir kafla 7 Yfirlit 7. hluta Margföldun tvíliða: stutt upprifjun Þáttun þríliða: stutt upprifjun Samanburður línulegra falla og vísisfalla: stutt upprifjun Yfirlit kafla 7: samantekt 7.1 Breytingamynstur 7.1.0 Yfirlit kennslustundar 7.1.1 Að koma auga á ný breytingamynstur 7.1.2 Tengsl lengdar og flatarmáls 7.1.3 Mælingar færðar í hnitakerfi 7.1.4 Inntak og úttak falls 7.1.5 Æfingar 7.1.6 Samantekt kennslustundar 7.2 Kynning á annars stigs tengslum 7.2.0 Yfirlit kennslustundar 7.2.1 Ferningar í rúmfræðilegu mynstri 7.2.2 Jöfn breyting og veldisbreyting 7.2.3 Annars stigs stæður 7.2.4 Annars stigs tengsl 7.2.5 Æfingar 7.2.6 Samantekt kennslustundar 7.3 Að ákvarða hvort fall sé annars stigs 7.3.0 Yfirlit kennslustundar 7.3.1 Annars stigs stæður og flatarmál 7.3.2 Jöfnur ritaðar fyrir mynstur með ferningum 7.3.3 Annars stigs runur 7.3.4 Er mynstrið annars stigs fall? 7.3.5 Æfingar 7.3.6 Samantekt kennslustundar 7.4 Samanburður annars stigs falla og veldisvísisfalla 7.4.0 Yfirlit kennslustundar 7.4.1 Samanburður stæðna 7.4.2 Línulegur vöxtur, veldisvöxtur og annars stigs vöxtur 7.4.3 Samanburður vísisfalla og annars stigs falla 7.4.4 Samanburður stæðna með veldisvísum og annars stigs stæðna 7.4.5 Æfingar 7.4.6 Samantekt kennslustundar 7.5 Smíði annars stigs falla til að lýsa aðstæðum, 1. hluti 7.5.0 Yfirlit kennslustundar 7.5.1 Talnamynstur 7.5.2 Annars stigs líkan fyrir tengsl tíma og vegalengdar 7.5.3 Vegalengd sem annars stigs fall af liðnum tíma 7.5.4 Annars stigs stæða sem lýsir tengslum vegalengdar og tíma 7.5.5 Æfingar 7.5.6 Samantekt kennslustundar 7.6 Smíði annars stigs falla til að lýsa aðstæðum, 2. hluti 7.6.0 Yfirlit kennslustundar 7.6.1 Að nota línuleg föll til að lýsa jöfnum hraða 7.6.2 Áhrif þyngdarafls á annars stigs föll 7.6.3 Að nota annars stigs föll til að lýsa hæð 7.6.4 Að túlka gröf annars stigs falla 7.6.5 Æfingar 7.6.6 Samantekt kennslustundar 7.7 Skilgreiningarmengi, myndmengi, topppunktur og núllstöðvar annars stigs falla 7.7.0 Yfirlit kennslustundar 7.7.1 Samanburður á gröfum falla 7.7.2 Líkanagerð með raunverulegum gögnum og annars stigs föllum 7.7.3 Skilgreiningarmengi, topppunktur og núllstöð annars stigs falla 7.7.4 Tengsl skilgreiningarmengis falls við graf þess 7.7.5 Æfingar 7.7.6 Samantekt kennslustundar 7.8 Jafngildar annars stigs stæður 7.8.0 Yfirlit kennslustundar 7.8.1 Flatarmálsmyndir 7.8.2 Dreifireglan notuð til að rita jafngildar stæður 7.8.3 Skýringarmyndir notaðar til að finna jafngildar annars stigs stæður 7.8.4 Að rita jafngildar stæður 7.8.5 Æfingar 7.8.6 Samantekt kennslustundar 7.9 Staðalform og þáttað form 7.9.0 Yfirlit kennslustundar 7.9.1 Að leysa jöfnur með andhverfum aðgerðum 7.9.2 Að finna margfeldi mismuna 7.9.3 Staðalform og þáttað form annars stigs stæðna 7.9.4 Stæður á staðalformi 7.9.5 Æfingar 7.9.6 Samantekt kennslustundar 7.10 Gröf falla á staðalformi og þáttuðu formi 7.10.0 Yfirlit kennslustundar 7.10.1 Gröf línulegra jafna 7.10.2 Form annars stigs stæðna og gröf þeirra 7.10.3 Skurðpunktar annars stigs stæðna við x- og y-ás 7.10.4 Að nota staðalform jöfnu til að finna skurðpunkta við x- og y-ás 7.10.5 Æfingar 7.10.6 Samantekt kennslustundar 7.11 Teikning grafs út frá þáttuðu formi 7.11.0 Yfirlit kennslustundar 7.11.1 Að finna hnit 7.11.2 Þáttað form annars stigs stæðu og skurðpunktar grafs hennar við x-ás 7.11.3 Graf annars stigs falls skissað með að minnsta kosti þremur þekktum punktum 7.11.4 Að nota topppunkt og samhverfuás annars stigs falla 7.11.5 Gröf annars stigs falla 7.11.6 Æfingar 7.11.7 Samantekt kennslustundar 7.12 Teikning grafs út frá staðalformi, 1. hluti 7.12.0 Yfirlit kennslustundar 7.12.1 Að nota stuðla og fastaliði til að bera kennsl á gröf línulegra jafna 7.12.2 Umbreytingar á annars stigs föllum 7.12.3 Að skilja hegðun grafs út frá annars stigs stæðu þess 7.12.4 Framsetningar annars stigs falla 7.12.5 Að bera kennsl á gröf annars stigs falla 7.12.6 Æfingar 7.12.7 Samantekt kennslustundar 7.13 Teikning grafs út frá staðalformi, 2. hluti 7.13.0 Yfirlit kennslustundar 7.13.1 Jafngildar stæður 7.13.2 Línulegi liðurinn í annars stigs stæðu 7.13.3 Að rita jöfnur sem tákna graf 7.13.4 Að rita annars stigs jöfnur út frá rauntölulausnum 7.13.5 Að teikna gröf annars stigs jafna 7.13.6 Æfingar 7.13.7 Samantekt kennslustundar 7.14 Gröf sem tákna aðstæður 7.14.0 Yfirlit kennslustundar 7.14.1 Að reikna gildi annars stigs falla í raunverulegu samhengi 7.14.2 Að túlka fallssamband milli tveggja stærða 7.14.3 Að greina föll með mismunandi framsetningum 7.14.4 Að nota annars stigs föll til að leysa verkefni 7.14.5 Að bera kennsl á lykileiginleika falla út frá grafi 7.14.6 Æfingar 7.14.7 Samantekt kennslustundar 7.15 Topppunktsform 7.15.0 Yfirlit kennslustundar 7.15.1 Að greina tvö sett af jöfnum 7.15.2 Topppunktsformið 7.15.3 Hnit topppunktsins 7.15.4 Graf falls á topppunktsformi 7.15.5 Æfingar 7.15.6 Samantekt kennslustundar 7.16 Teikning grafs út frá topppunktsformi 7.16.0 Yfirlit kennslustundar 7.16.1 Þrjú form annars stigs stæðna 7.16.2 Að teikna föll á topppunktsformi 7.16.3 Annars stigs jöfnur og gröf 7.16.4 Skissun grafs út frá jöfnu 7.16.5 Æfingar 7.16.6 Samantekt kennslustundar 7.17 Breyting á topppunkti 7.17.0 Yfirlit kennslustundar 7.17.1 Annars stigs stæður á mismunandi formum 7.17.2 Breyting stæðna til að hliðra gröfum 7.17.3 Breyting á stikum annars stigs stæðu 7.17.4 Umbreyting grunnfallsins 7.17.5 Jöfnur grafhliðrana 7.17.6 Æfingar 7.17.7 Samantekt kennslustundar Verkefni 7: Hönnun gosbrunns Yfirlit verkefnis 7 Kynning á hönnun gosbrunns Hönnun gosbrunns Samantekt 7. hluta 8 Annars stigs jöfnur Hluti 8 Yfirlit og undirbúningur Yfirlit 8. hluta Rita jafngildar stæður: Upprifjun úr smákennslu Finna skurðpunkta við ása: Upprifjun úr smákennslu Pöra gröf annars stigs falla við jöfnur þeirra: Upprifjun úr smákennslu Yfirlit 8. hluta: Samantekt 8.1 Finna óþekkt inntaksgildi 8.1.0 Yfirlit kennslustundar 8.1.1 Skilningur á aðstæðum með annars stigs jöfnum 8.1.2 Gerð líkans fyrir annars stigs vandamál 8.1.3 Setja fram annars stigs jöfnu sem lýsir líkaninu 8.1.4 Túlkun lausnar 8.1.5 Æfing 8.1.6 Samantekt kennslustundar 8.2 Hvenær og hvers vegna ritum við annars stigs jöfnur? 8.2.0 Yfirlit kennslustundar 8.2.1 Túlkun jafna í samhengi 8.2.2 Kanna aðferðir án grafa til að leysa annars stigs jöfnur 8.2.3 Lausn annars stigs jöfnu sem er sett jöfn núlli 8.2.4 Lausn raunverulegra vandamála með annars stigs jöfnum 8.2.5 Æfing 8.2.6 Samantekt kennslustundar 8.3 Leysa annars stigs jöfnur með röksemdafærslu 8.3.0 Yfirlit kennslustundar 8.3.1 Ákvörðun fjölda lausna 8.3.2 Að þekkja lausnapör 8.3.3 Lausn flóknari annars stigs jafna 8.3.4 Að finna lausnirnar 8.3.5 Æfing 8.3.6 Samantekt kennslustundar 8.4 Leysa annars stigs jöfnur með núllþáttareglunni 8.4.0 Yfirlit kennslustundar 8.4.1 Kynning á núllþáttareglunni 8.4.2 Lausn jafna með vaxandi flækjustigi með röksemdafærslu 8.4.3 Beiting núllþáttareglu til að leysa raunverulegt kastvandamál 8.4.4 Lausn jafna með núllþáttareglu og röksemdafærslu 8.4.5 Æfing 8.4.6 Samantekt kennslustundar 8.5 Hversu margar lausnir? 8.5.0 Yfirlit kennslustundar 8.5.1 Upprifjun á núllþáttareglunni 8.5.2 Túlkun grafa til að leysa annars stigs jöfnur 8.5.3 Val á árangursríkri aðferð til að leysa annars stigs jöfnur 8.5.4 Greining villna við lausn annars stigs jafna 8.5.5 Æfing 8.5.6 Samantekt kennslustundar 8.6 Endurrita annars stigs stæður á þáttað form, hluti 1 8.6.0 Yfirlit kennslustundar 8.6.1 Að finna og rökstyðja óþekkta þætti 8.6.2 Notkun skýringarmynda til að skilja jafngildar stæður 8.6.3 Umritun annars stigs stæðna á staðalform 8.6.4 Að finna tölur sem vantar í pör jafngildra stæðna 8.6.5 Æfing 8.6.6 Samantekt kennslustundar 8.7 Endurrita annars stigs stæður á þáttað form, hluti 2 8.7.0 Yfirlit kennslustundar 8.7.1 Skilningur á summum og margfeldum heiltalna 8.7.2 Túlkun neikvæðra fastaliða við þáttun annars stigs stæðna 8.7.3 Greining þátta í 100 og -100 8.7.4 Að finna liði sem vantar 8.7.5 Æfing 8.7.6 Samantekt kennslustundar 8.8 Endurrita annars stigs stæður á þáttað form, hluti 3 8.8.0 Yfirlit kennslustundar 8.8.1 Mat á stæðum með hugarreikningi 8.8.2 Að þekkja liðað margfeldi mismunar tveggja ferninga 8.8.3 Þáttun annars stigs jafna án fyrsta stigs liðar 8.8.4 Ákvörðun um hvort hægt sé að umrita stæðu á þáttað form 8.8.5 Æfing 8.8.6 Samantekt kennslustundar 8.9 Leysa annars stigs jöfnur með því að nota þáttað form 8.9.0 Yfirlit kennslustundar 8.9.1 Að finna lausn með innsetningu 8.9.2 Notkun þáttaðs forms og núllþáttareglu til að leysa annars stigs jöfnur 8.9.3 Ritun jöfnu sem lýsir annars stigs falli með aðeins eina lausn 8.9.4 Lausn fleiri annars stigs jafna 8.9.5 Æfing 8.9.6 Samantekt kennslustundar 8.10 Endurrita annars stigs stæður á þáttað form, hluti 4 8.10.0 Yfirlit kennslustundar 8.10.1 Greining ýmissa annars stigs stæðna 8.10.2 Vinna með þáttað form annars stigs stæðna með forystustuðul annan en einn 8.10.3 Notkun tækni til að finna ræða þætti 8.10.4 Að finna þætti annars stigs stæðna á staðalformi 8.10.5 Lausn annars stigs jafna með hvaða aðferð sem er 8.10.6 Æfing 8.10.7 Samantekt kennslustundar 8.11 Rita annars stigs jöfnur út frá rauntölulausnum 8.11.0 Yfirlit kennslustundar 8.11.1 Tengsl annars stigs falls og núllstöðva þess 8.11.2 Að finna annars stigs fall út frá núllstöðvum þess 8.11.3 Að finna annars stigs fall út frá núllstöðvum þess og punkti 8.11.4 Að rita annars stigs föll út frá ólíkum upplýsingum 8.11.5 Æfingar 8.11.6 Samantekt kennslustundar 8.12 Nota tækni til að finna annars stigs aðhvarf 8.12.0 Yfirlit kennslustundar 8.12.1 Að teikna graf gagnasafns með annars stigs mynstri með tækni 8.12.2 Að finna feril sem fellur best að gögnunum 8.12.3 Að spá fyrir með annars stigs líkani 8.12.4 Að finna gögn sem vantar í safnið 8.12.5 Æfingar 8.12.6 Samantekt kennslustundar Verkefni 8: Líkan af flugi eldflaugar Yfirlit verkefnis 8 Tengsl núllstöðva við þáttað form annars stigs jafna Umbreyting milli þáttaðs forms og staðalforms Líkan af flugi eldflaugar með annars stigs jöfnu Samantekt 8. hluta 9.11 Notkun annars stigs stæðna á topppunktsformi til að leysa verkefni 9.11.0 Yfirlit kennslustundar 9.11.1 Hágildi og lággildi falls 9.11.2 Táknar topppunkturinn lággildi eða hágildi? 9.11.3 Samanburður á hágildum annars stigs falla 9.11.4 Hágildi, lággildi og greining á topppunkti 9.11.5 Æfingar 9.11.6 Samantekt kennslustundar 9 Fleiri annars stigs jöfnur Hluti 9 Yfirlit og undirbúningur Yfirlit 9. hluta Einfalda rætur: Upprifjun úr smákennslu Þáttun þríliða sem eru ferningar tvíliða: Upprifjun úr smákennslu Umbreytingar: Upprifjun úr smákennslu Yfirlit 9. hluta: Samantekt 9.1 Hvað eru fullkomnir ferningar? 9.1.0 Yfirlit kennslustundar 9.1.1 Jöfnur með annars stigs stæðum báðum megin jafnaðarmerkis 9.1.2 Að þekkja uppbyggingu stæðna sem eru ferningar 9.1.3 Að leysa fjölþrepa annars stigs jöfnur með ferningum 9.1.4 Að útskýra hvers vegna stæða er ferningur 9.1.5 Æfingar 9.1.6 Samantekt kennslustundar 9.2 Að fylla í ferninginn, hluti 1 9.2.0 Yfirlit kennslustundar 9.2.1 Mismunandi form stæðna sem eru ferningar 9.2.2 Staðalform og þáttað form stæðna sem eru ferningar 9.2.3 Að fylla í ferninginn 9.2.4 Að búa til stæðu sem er ferningur 9.2.5 Æfingar 9.2.6 Samantekt kennslustundar 9.3 Að fylla í ferninginn, hluti 2 9.3.0 Yfirlit kennslustundar 9.3.1 Að leysa jöfnur með brotum 9.3.2 Að nota aðferðina að fylla í ferninginn til að leysa jöfnur 9.3.3 Að leysa með því að fylla í ferninginn 9.3.4 Að fylla í ferninginn með brotum 9.3.5 Æfingar 9.3.6 Samantekt kennslustundar 9.4 Að fylla í ferninginn, hluti 3 9.4.0 Yfirlit kennslustundar 9.4.1 Stæður sem eru ferningar með stuðla aðra en 1 9.4.2 Að umrita stæður í öðru veldi 9.4.3 Staðalform og þættir í öðru veldi 9.4.4 Þrjár mismunandi aðferðir til að leysa jöfnu 9.4.5 Stæða sem er ferningur og þættir í öðru veldi 9.4.6 Æfingar 9.4.7 Samantekt kennslustundar 9.5 Annars stigs jöfnur með óræðum lausnum 9.5.0 Yfirlit kennslustundar 9.5.1 Rætur ferninga 9.5.2 Lausnir ritaðar sem ferningsrætur 9.5.3 Óræðar lausnir fundnar með því að fylla í ferninginn 9.5.4 Nákvæmar lausnir fundnar 9.5.5 Æfingar 9.5.6 Samantekt kennslustundar 9.6 Jöfnuformúla annars stigs jafna 9.6.0 Yfirlit kennslustundar 9.6.1 Mat á stæðum 9.6.2 Besta aðferðin valin til að leysa jöfnu 9.6.3 Jöfnuformúla annars stigs jafna 9.6.4 Jöfnur leystar með jöfnuformúlu annars stigs jafna 9.6.5 Æfingar 9.6.6 Samantekt kennslustundar 9.7 Notkun á jöfnuformúlu annars stigs jafna 9.7.0 Yfirlit kennslustundar 9.7.1 Mat á stæðum með breytum 9.7.2 Algengar reiknivillur við notkun jöfnuformúlu annars stigs jafna 9.7.3 Mismunandi aðferðir til að athuga lausnir annars stigs jafna 9.7.4 Æfingar í að finna reiknivillur 9.7.5 Æfingar 9.7.6 Samantekt kennslustundar 9.8 Útleiðsla á jöfnuformúlu annars stigs jafna 9.8.0 Yfirlit kennslustundar 9.8.1 Útleiðsla á jöfnuformúlu annars stigs jafna, hluti 1 9.8.2 Útleiðsla á jöfnuformúlu annars stigs jafna, hluti 2 9.8.3 Að skilja að jöfnuformúla annars stigs jafna er samsett úr skrefum þess að fylla í ferninginn 9.8.4 Æfingar 9.8.5 Samantekt kennslustundar 9.9 Ritun annars stigs jafna á mismunandi formum 9.9.0 Yfirlit kennslustundar 9.9.1 Topppunktur fundinn út frá topppunktsformi 9.9.2 Mismunandi form annars stigs stæðna 9.9.3 Topppunktsform út frá topppunkti og punkti 9.9.4 Endurritun annars stigs stæðna 9.9.5 Æfingar 9.9.6 Samantekt kennslustundar 9.10 Endurritun annars stigs stæðna á topppunktsformi 9.10.0 Yfirlit kennslustundar 9.10.1 Topppunktur og skurðpunktar falls 9.10.2 Liðun úr þáttuðu formi yfir á staðalform 9.10.3 Að breyta úr staðalformi í topppunktsform 9.10.4 Að endurrita stæður á topppunktsformi 9.10.5 Mismunandi form annars stigs stæðna 9.10.6 Topppunktsform og hnit topppunktsins 9.10.7 Æfingar 9.10.8 Samantekt kennslustundar Verkefni 9: Notkun annars stigs jafna til að búa til líkön og leysa verkefni Yfirlit verkefnis 9 Jöfnur tveggja lína og ferils Greining á dýfingarstökki Línulegt fall og annars stigs fall Hagnaður af fljótsiglingu Samantekt 9. hluta Rannsóknir í framkvæmd Uppbyggileg barátta Uppbyggileg mistök Samvinnunám og uppbyggileg umræða Umræður í kennslustofunni Áhugahvöt í kennslustofu Gróskuhugarfar Markmiðasetning Metavitund Dreifð upprifjun Margmiðlunarnámskenningin Margmiðlunarreglan Reglan um skapandi nám Viðauki Hönnun námskeiðs Röð eininga og úrræði Uppbygging kennslustunda og úrræði Tegundir námsmats og úrræði Atriðisorðaskrá$RB=[];$RV=function(a){$RT=performance.now();for(var b=0;b<a.length;b+=2){var c=a[b],e=a[b+1];null!==e.parentNode&&e.parentNode.removeChild(e);var f=c.parentNode;if(f){var g=c.previousSibling,h=0;do{if(c&&8===c.nodeType){var d=c.data;if("/$"===d||"/&"===d)if(0===h)break;else h--;else"$"!==d&&"$?"!==d&&"$~"!==d&&"$!"!==d&&"&"!==d||h++}d=c.nextSibling;f.removeChild(c);c=d}while(c);for(;e.firstChild;)f.insertBefore(e.firstChild,c);g.data="$";g._reactRetry&&requestAnimationFrame(g._reactRetry)}}a.length=0};
$RC=function(a,b){if(b=document.getElementById(b))(a=document.getElementById(a))?(a.previousSibling.data="$~",$RB.push(a,b),2===$RB.length&&("number"!==typeof $RT?requestAnimationFrame($RV.bind(null,$RB)):(a=performance.now(),setTimeout($RV.bind(null,$RB),2300>a&&2E3<a?2300-a:$RT+300-a)))):b.parentNode.removeChild(b)};$RC("B:0","S:0")Algebra 1 (IS) Kafli 5 5.12.4 Möguleg jafna falls út frá grafi 5 5.12 Röksemdafærsla um veldisgröf, hluti 1 5.12.4 Möguleg jafna falls út frá grafi FYRRI KAFLI 5.12.3 Gröf sem tákna vísishnignun NÆSTI KAFLI 5.12.5 Æfingar 5.12.4 - Möguleg jafna falls út frá grafi Lokaverkefni Lokaverkefni Skoðaðu gröfin þrjú sem tákna vísisföllin f, g og h. Föllin f og h eru skilgreind með jöfnunum: f (x) = 10 \cdot 2^{x} h (x) = 20 \cdot 4^{x} Hver af eftirfarandi jöfnum gæti skilgreint fallið g? Undirbúðu rökstuðninginn þinn. g (x) = 20 \cdot {(1,5)}^{x} g (x) = 20 \cdot {(2,5)}^{x} g (x) = 10 \cdot {(3,5)}^{x} g (x) = 20 \cdot {(4,5)}^{x} Svar: g (x) = 20 \cdot {(2,5)}^{x} Útskýrðu rökstuðninginn þinn. Lausn Berðu svarið þitt saman: Graf g hefur sama skurðpunkt við y-ás og graf h, sem er 20. Það vex hraðar en f en hægar en h, svo vaxtarstuðullinn hlýtur að vera stærri en 2 en minni en 4. 2 b4FYRRI KAFLI 5.12.3 Gröf sem tákna vísishnignun NÆSTI KAFLI 5.12.5 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Fallið f byrjar neðar á y-ás og vex hægar en hin tvö.\",\"src\":\"https://m4u5rs6quwqmofe9.public.blob.vercel-storage.com/openstax/algebra-1/is/c91699a5862502edaffc0fc9cafd5d89472eebad.jpg?v=c91699a58625\",\"resourceId\":\"c91699a5862502edaffc0fc9cafd5d89472eebad\",\"__legacyMedia\":true,\"width\":400,\"height\":372},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"generated-2-children-3\",\"typeKey\":\"Paragraph\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"Föllin f og h eru skilgreind með jöfnunum:\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eFöllin f og h eru skilgreind með jöfnunum:\u003c/p\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"eq-5-12-4-f\",\"typeKey\":\"EquationBlock\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"f(x) = 10\cdot2^x\",\"props\":{\"latex\":\"f(x)=10\\\\cdot2^x\",\"mathml\":\"\u003cmath display=\\\"block\\\"\u003e\u003cmrow\u003e\u003cmi\u003ef\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003cmo\u003e\cdot\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/math\u003e\",\"displayMode\":true},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"eq-5-12-4-h\",\"typeKey\":\"EquationBlock\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"h(x) = 20\cdot4^x\",\"props\":{\"latex\":\"h(x)=20\\\\cdot4^x\",\"mathml\":\"\u003cmath display=\\\"block\\\"\u003e\u003cmrow\u003e\u003cmi\u003eh\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e20\u003c/mn\u003e\u003cmo\u003e\cdot\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e4\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/math\u003e\",\"displayMode\":true},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"generated-2-children-6\",\"typeKey\":\"Paragraph\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"Hver af eftirfarandi jöfnum gæti skilgreint fallið g? Undirbúðu rökstuðninginn þinn.\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eHver af eftirfarandi jöfnum gæti skilgreint fallið g? Undirbúðu rökstuðninginn þinn.\u003c/p\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"eq-5-12-4-choice-a\",\"typeKey\":\"EquationBlock\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"g(x) = 20\cdot(1,5)^x\",\"props\":{\"latex\":\"g(x)=20\\\\cdot(1.5)^x\",\"mathml\":\"\u003cmath display=\\\"block\\\"\u003e\u003cmrow\u003e\u003cmi\u003eg\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e20\u003c/mn\u003e\u003cmo\u003e\cdot\u003c/mo\u003e\u003cmsup\u003e\u003cmrow\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmn\u003e1,5\u003c/mn\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/math\u003e\",\"displayMode\":true},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"eq-5-12-4-choice-b\",\"typeKey\":\"EquationBlock\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"g(x) = 20\cdot(2,5)^x\",\"props\":{\"latex\":\"g(x)=20\\\\cdot(2.5)^x\",\"mathml\":\"\u003cmath display=\\\"block\\\"\u003e\u003cmrow\u003e\u003cmi\u003eg\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e20\u003c/mn\u003e\u003cmo\u003e\cdot\u003c/mo\u003e\u003cmsup\u003e\u003cmrow\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmn\u003e2,5\u003c/mn\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/math\u003e\",\"displayMode\":true},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"eq-5-12-4-choice-c\",\"typeKey\":\"EquationBlock\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"g(x) = 10\cdot(3,5)^x\",\"props\":{\"latex\":\"g(x)=10\\\\cdot(3.5)^x\",\"mathml\":\"\u003cmath display=\\\"block\\\"\u003e\u003cmrow\u003e\u003cmi\u003eg\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003cmo\u003e\cdot\u003c/mo\u003e\u003cmsup\u003e\u003cmrow\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmn\u003e3,5\u003c/mn\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/math\u003e\",\"displayMode\":true},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"eq-5-12-4-choice-d\",\"typeKey\":\"EquationBlock\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"g(x) = 20\cdot(4,5)^x\",\"props\":{\"latex\":\"g(x)=20\\\\cdot(4.5)^x\",\"mathml\":\"\u003cmath display=\\\"block\\\"\u003e\u003cmrow\u003e\u003cmi\u003eg\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e20\u003c/mn\u003e\u003cmo\u003e\cdot\u003c/mo\u003e\u003cmsup\u003e\u003cmrow\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmn\u003e4,5\u003c/mn\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/math\u003e\",\"displayMode\":true},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"generated-2-children-11\",\"typeKey\":\"Paragraph\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"Svar:\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eSvar:\u003c/p\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"eq-5-12-4-answer\",\"typeKey\":\"EquationBlock\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"g(x) = 20\cdot(2,5)^x\",\"props\":{\"latex\":\"g(x)=20\\\\cdot(2.5)^x\",\"mathml\":\"\u003cmath display=\\\"block\\\"\u003e\u003cmrow\u003e\u003cmi\u003eg\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e20\u003c/mn\u003e\u003cmo\u003e\cdot\u003c/mo\u003e\u003cmsup\u003e\u003cmrow\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmn\u003e2,5\u003c/mn\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/math\u003e\",\"displayMode\":true},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"generated-2-children-13\",\"typeKey\":\"Paragraph\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"Útskýrðu rökstuðninginn þinn.\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eÚtskýrðu rökstuðninginn þinn.\u003c/p\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"generated-2-children-14\",\"typeKey\":\"Paragraph\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"Berðu svarið þitt saman:\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eBerðu svarið þitt saman:\u003c/p\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"generated-2-children-15\",\"typeKey\":\"Paragraph\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"Graf g hefur sama skurðpunkt við y-ás og graf h, sem er 20. Það vex hraðar en f en hægar en h, svo vaxtarstuðullinn hlýtur að vera stærri en 2 en minni en 4.\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eGraf g hefur sama skurðpunkt við y-ás og graf h, sem er 20. Það vex hraðar en f en hægar en h, svo vaxtarstuðullinn hlýtur að vera stærri en 2 en minni en 4.\u003c/p\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"eq-5-12-4-bounds\",\"typeKey\":\"EquationBlock\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"2 \u003c b \u003c 4\",\"props\":{\"latex\":\"2\u003cb\u003c4\",\"mathml\":\"\u003cmath display=\\\"block\\\"\u003e\u003cmrow\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmo\u003e\u003c\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e\u003c\u003c/mo\u003e\u003cmn\u003e4\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\",\"displayMode\":true},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]}]}],\"sectionNodeId\":\"fa2f5711-6537-47da-a2f4-9b26cd427123\",\"bookSlug\":\"algebra-1\",\"sectionSlug\":\"5-12-4-possible-equation-for-a-function-on-a-graph\",\"locale\":\"is\",\"renderModel\":{\"surface\":\"READER\",\"nodes\":[{\"blockId\":\"page_6729ab16-b788-4137-ac3b-733b3dabef62_title_reviewed\",\"typeKey\":\"Heading\",\"variant\":null,\"orderIndex\":0,\"tokenRefs\":[\"typography.heading\",\"spacing.block\"],\"text\":\"5.12.4 Möguleg jafna falls út frá grafi\",\"props\":{\"level\":2},\"children\":[]},{\"blockId\":\"generated-1\",\"typeKey\":\"Paragraph\",\"variant\":null,\"orderIndex\":1,\"tokenRefs\":[\"typography.body\",\"spacing.block\"],\"text\":\"5.12.4 - Möguleg jafna falls út frá grafi\",\"props\":{\"__sourceHtml\":\"\u003cp\u003e5.12.4 - Möguleg jafna falls út frá grafi\u003c/p\u003e\"},\"children\":[]},{\"blockId\":\"sect-5-12-4-cooldown\",\"typeKey\":\"Section\",\"variant\":null,\"orderIndex\":2,\"tokenRefs\":[\"spacing.section\"],\"text\":\"Lokaverkefni\",\"props\":{\"title\":\"Lokaverkefni\",\"depth\":\"1\"},\"children\":[{\"blockId\":\"generated-2-children-0\",\"typeKey\":\"Paragraph\",\"variant\":null,\"orderIndex\":3,\"tokenRefs\":[\"typography.body\",\"spacing.block\"],\"text\":\"Lokaverkefni\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eLokaverkefni\u003c/p\u003e\"},\"children\":[]},{\"blockId\":\"generated-2-children-1\",\"typeKey\":\"Paragraph\",\"variant\":null,\"orderIndex\":4,\"tokenRefs\":[\"typography.body\",\"spacing.block\"],\"text\":\"Skoðaðu gröfin þrjú sem tákna vísisföllin f, g og h.\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eSkoðaðu gröfin þrjú sem tákna vísisföllin f, g og h.\u003c/p\u003e\"},\"children\":[]},{\"blockId\":\"media-5-12-4-graphs\",\"typeKey\":\"Figure\",\"variant\":\"default\",\"orderIndex\":5,\"tokenRefs\":[\"figure.default\",\"typography.caption\"],\"text\":\"Graf þriggja vísisvaxtarfalla í hnitakerfi. Föllin g og h skerast við y-ás í sama punkti, en h vex hraðast. Fallið f byrjar neðar á y-ás og vex hægar en hin tvö.\",\"props\":{\"alt\":\"Graf þriggja vísisvaxtarfalla í hnitakerfi. Föllin g og h skerast við y-ás í sama punkti, en h vex hraðast. Fallið f byrjar neðar á y-ás og vex hægar en hin tvö.\",\"src\":\"https://m4u5rs6quwqmofe9.public.blob.vercel-storage.com/openstax/algebra-1/is/c91699a5862502edaffc0fc9cafd5d89472eebad.jpg?v=c91699a58625\",\"resourceId\":\"c91699a5862502edaffc0fc9cafd5d89472eebad\",\"__legacyMedia\":true,\"width\":400,\"height\":372},\"children\":[]},{\"blockId\":\"generated-2-children-3\",\"typeKey\":\"Paragraph\",\"variant\":null,\"orderIndex\":6,\"tokenRefs\":[\"typography.body\",\"spacing.block\"],\"text\":\"Föllin f og h eru skilgreind með jöfnunum:\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eFöllin f og h eru skilgreind með jöfnunum:\u003c/p\u003e\"},\"children\":[]},{\"blockId\":\"eq-5-12-4-f\",\"typeKey\":\"EquationBlock\",\"variant\":null,\"orderIndex\":7,\"tokenRefs\":[\"math.block\"],\"text\":\"f(x) = 10\cdot2^x\",\"props\":{\"latex\":\"f(x)=10\\\\cdot2^x\",\"mathml\":\"\u003cmath display=\\\"block\\\"\u003e\u003cmrow\u003e\u003cmi\u003ef\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003cmo\u003e\cdot\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/math\u003e\",\"displayMode\":true},\"children\":[]},{\"blockId\":\"eq-5-12-4-h\",\"typeKey\":\"EquationBlock\",\"variant\":null,\"orderIndex\":8,\"tokenRefs\":[\"math.block\"],\"text\":\"h(x) = 20\cdot4^x\",\"props\":{\"latex\":\"h(x)=20\\\\cdot4^x\",\"mathml\":\"\u003cmath display=\\\"block\\\"\u003e\u003cmrow\u003e\u003cmi\u003eh\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e20\u003c/mn\u003e\u003cmo\u003e\cdot\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e4\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/math\u003e\",\"displayMode\":true},\"children\":[]},{\"blockId\":\"generated-2-children-6\",\"typeKey\":\"Paragraph\",\"variant\":null,\"orderIndex\":9,\"tokenRefs\":[\"typography.body\",\"spacing.block\"],\"text\":\"Hver af eftirfarandi jöfnum gæti skilgreint fallið g? Undirbúðu rökstuðninginn þinn.\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eHver af eftirfarandi jöfnum gæti skilgreint fallið g? Undirbúðu rökstuðninginn þinn.\u003c/p\u003e\"},\"children\":[]},{\"blockId\":\"eq-5-12-4-choice-a\",\"typeKey\":\"EquationBlock\",\"variant\":null,\"orderIndex\":10,\"tokenRefs\":[\"math.block\"],\"text\":\"g(x) = 20\cdot(1,5)^x\",\"props\":{\"latex\":\"g(x)=20\\\\cdot(1.5)^x\",\"mathml\":\"\u003cmath display=\\\"block\\\"\u003e\u003cmrow\u003e\u003cmi\u003eg\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e20\u003c/mn\u003e\u003cmo\u003e\cdot\u003c/mo\u003e\u003cmsup\u003e\u003cmrow\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmn\u003e1,5\u003c/mn\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/math\u003e\",\"displayMode\":true},\"children\":[]},{\"blockId\":\"eq-5-12-4-choice-b\",\"typeKey\":\"EquationBlock\",\"variant\":null,\"orderIndex\":11,\"tokenRefs\":[\"math.block\"],\"text\":\"g(x) = 20\cdot(2,5)^x\",\"props\":{\"latex\":\"g(x)=20\\\\cdot(2.5)^x\",\"mathml\":\"\u003cmath display=\\\"block\\\"\u003e\u003cmrow\u003e\u003cmi\u003eg\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e20\u003c/mn\u003e\u003cmo\u003e\cdot\u003c/mo\u003e\u003cmsup\u003e\u003cmrow\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmn\u003e2,5\u003c/mn\u003e\u003cmo 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