Parallelforskydning af grafer

Introduktion
Dette arbejdsark er lavet til at give dig en forståelse af [b]parallelforskydning af grafer[/b]. Arbejdsarket er opbygget af en række opgaver, hvor du løbende skal "tænke matematik" og svare på spørgsmål, som skal hjælpe dig med at forstå.[br]En god idé kan derfor være at arbejde arbejdsarket igennem i par, så du har én at diskutere med, så I kan afprøve hinandens forståelse.
Parallelforskydning: Betydning
[b]Parallelforskydning [/b]betyder, at et objekt, en graf eller andet er [b]flyttet vandret og/eller lodret[/b], men [b]ikke er ændret[/b]. [br]Parallelforskydning betyder altså, at vi flytter noget vandret og/eller lodret, men vi laver ingen ændring som f.eks. at spejle eller fordreje.[br][br]Nedenfor er linjestykker [i]l[/i] forskudt henholdsvis:[br] Blå:  2 ned ad[br] Orange:  6 til højre[br] Magenta: 2 ned og 6 til højre[br][br][img]data:image/png;base64,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[/img]
Opvamrning (opgaven kommer nedenfor)
Opvarmning
Funktionen [math]g[/math] er en parallelforskydning af [math]f[/math]:[br][br][math]g(x)=f(x)-3[/math][br][br]Hvordan tror du, at grafen for [math]g[/math] ser ud?[br][i]Tegn på figuren ovenfor, hvis det hjælper dig med at tænke.[/i]
Indtegn punkter (opgaven kommer nedenfor)
Indtegn punkter
Funktion [math]g[/math] er en parallelforskydning af [math]f[/math]:[br][br][math]g(x)=f(x)-3[/math][br][br]Adam har lavet en tabel med støttepunkter til [math]g[/math].[br][br] a) [b]Diskutér:[/b] Hvordan har Adam beregnet [math]g(-5)[/math]?[br][br] b) Fuldfør tabellen for at tegne flere støttepunkter til [math]g[/math]. Skriv [b]Færdig[/b] eller et spørgsmål i feltet nedenfor.[br]  [i]Udfyld der, hvor der er spørgsmålstegn. For at skifte celle, skal du muligvis trykke på 'ESC', inden du skifter.[/i]
Ram punkterne (opgaven kommer nedenfor)
Ram punkterne
Forskriften [math]g(x)[/math] er udtrykt ved hjælp af [math]f(x)[/math].[br][br] a) Prøv at skrive [math]g(x)=f(x)-3[/math] i Input-feltet ovenfor. Hvordan ser grafen ud?[br][br] b) Ændr udtrykket så grafen for [math]g[/math] rammer alle punkterne.
Ram punkterne 2 (opgaven kommer nedenfor)
Ram punkterne 2
Funktionen [math]z[/math] er en parallelforskydning af [math]w[/math].[br][br]Opskriv en forskrift [math]z(x)[/math] (udtrykt ved [math]w(x)[/math]), så grafen for [math]z[/math] rammer alle punkterne.
Forudsig grafen (opgaven kommer nedenfor)
Forudsig grafen
Funktion [math]h[/math] er en parallelforskydning af [math]f[/math]:[br][br][math]h(x)=f(x-3)[/math][br][br] a) [b]Diskutér:[/b] Hvordan tror du, at grafen for [math]h[/math] ser ud?[br][br] b) Beregn værdien af [math]h(2)[/math]. Indsæt dit svar og forklaring.
Børges løsning (opgaven kommer nedenfor)
Børges løsning
Funktion [math]h[/math] er en parallelforskydning af [math]f[/math]:[br][br][math]h(x)=f(x-3)[/math][br][br]Figuren ovenfor viser, hvordan Børge bestemte, at [math]h(2)=1[/math].[br][br] a) [b]Diskutér:[/b] Hvad var Børges strategi?[br][br] b) Hvordan vil Børge bestemme værdien af [math]h(5)[/math]?.
Indtegn punkter 2 (opgaven kommer nedenfor)
Indtegn punkter 2
Funktion [math]h[/math] er en parallelforskydning af [math]f[/math]:[br][br][math]h(x)=f(x-3)[/math][br][br]Fuldfør tabellen for at tegne flere støttepunkter til [math]h[/math]. Skriv [b]Færdig[/b] eller et spørgsmål i feltet nedenfor.[br][i]Udfyld der, hvor der er spørgsmålstegn. For at skifte celle, skal du muligvis trykke på 'ESC', inden du skifter.[/i]
Vandret parallelforskydning til højre (opgaven kommer nedenfor)
Vandret parallelforskydning til højre
Funktion [math]h[/math] er en parallelforskydning af [math]f[/math]:[br][br][math]h(x)=f(x-3)[/math][br][br]Forklar, hvorfor funktionen [math]h[/math] er parallelforskudt med 3 mod højre i forhold til [math]f[/math][i].[/i]
Ram punkterne 3 (opgaven kommer nedenfor)
Ram punkterne 3
Funktionen [math]t[/math] er en parallelforskydning af [math]c[/math].[br][br]Opskriv en forskrift [math]t(x)[/math] (udtrykt ved [math]c(x)[/math]), så grafen for [math]t[/math] rammer alle punkterne.
Lodret OG vandret parallelforskydning (opgaven kommer nedenfor)
Lodret OG Vandret parallelforskydning
Funktionen [math]g[/math] er en parallelforskydning 3 enheder op og 2 enheder til venstre af [math]f[/math].[br][br]Hvilken af forskrifterne passer til [math]g[/math]?
Parallelforskydning: Sætning
Nedenfor er sætningen fra bogen om parallelforskydning.[br][br]Forklar med dine egne ord, hvad sætningen siger.[br][br][img]data:image/png;base64,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[/img]
Flere opgaver (opgaven kommer nedenfor)
Flere opgaver
Den røde graf ovenfor er en parallelforskydning af grafen for [math]f[/math].[br][br]Angiv en forskrift for funktionen der hører til den røde graf.[br][i]Anvend skyderne til at tjekke dit svar.[br][br][/i]Gentag for hhv. den blå, grønne og magenta graf.
Parallelforskydning af parabel (opgaven kommer nedenfor)
Parallelforskydning af parablen (Toppunkt)
a) Forklar, at parablen hørende til andengradspolynomiet med forskrift [math]f\left(x\right)=x^2[/math] har toppunkt i [math]T\left(0,0\right)[/math].[br][br]b) Forklar, hvorfor parablen hørende til andengradspolynomiet med forskrift [math]g\left(x\right)=\left(x-p\right)^2+k[/math] har toppunkt i [math]T\left(p,k\right)[/math]. [i]Du kan anvende animationen ovenfor til hjælp.[br][/i][br]c) [b]BEVIS[/b], at andengradspolynomiet [math]p\left(x\right)=a\left(x-p\right)^2+k[/math] har toppunkt i [math]T\left(p,k\right)[/math][br] [i]Beviset laves på en tavle eller et stykke papir.[/i]
Exit Ticket: Hvor godt har du forstået parallelforskydning af grafer?
Hvor godt forstod du parallelforskydning af grafer?
Exit Ticket: Hvordan fungerede arbejdsformen med det online arbejdsark?
Hvor godt forstod du parallelforskydning af grafer?
Kommentar til emnet eller modulet?
Kommentar til emnet eller modulet?
Cerrar
– cals_1, Rasmus Gross Søgaard

Información: Parallelforskydning af grafer