Function Transformations Quiz Review - Lexington...
8
Math 2B/3A Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434 Name: Date: 1 Function Transformations Quiz Review Students Will Be Able To: • Recognize the basic graphs including: = , = ! , = ! , = , = 2 ! , = , and = ! ! . • Translate basic graphs up down, left and right and determine the resultant equation. • Reflect basic graphs over the x-axis or the y-axis. • Dilate (stretch or shrink) graphs by a given factor. • Compose multiple transformations. • Review Topic: Write equations for quadratic functions given a written description. Basic Graphs: Sketch each of the basic graphs below. Show at least 3, preferably 5 specific points. = = ! = ! = = = 1 = 2 !
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Transcript of Function Transformations Quiz Review - Lexington...
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434
Name: Date:
1
FunctionTransformationsQuizReview
StudentsWillBeAbleTo:
• Recognizethebasicgraphsincluding:𝑦 = 𝑥,𝑦 = 𝑥!,𝑦 = 𝑥!,𝑦 = 𝑥 ,𝑦 = 2! ,𝑦 = 𝑥, and𝑦 = !
!.
• Translatebasicgraphsupdown,leftandrightanddeterminetheresultantequation.• Reflectbasicgraphsoverthex-axisorthey-axis.• Dilate(stretchorshrink)graphsbyagivenfactor.• Composemultipletransformations.• ReviewTopic:Writeequationsforquadraticfunctionsgivenawrittendescription.
BasicGraphs:Sketcheachofthebasicgraphsbelow.Showatleast3,preferably5specificpoints.
𝑦 = 𝑥
𝑦 = 𝑥!
𝑦 = 𝑥!
𝑦 = 𝑥
𝑦 = 𝑥
𝑦 = 1𝑥
𝑦 = 2!
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434
Name: Date:
2
ReferenceInformationTranslationsof𝑦 = 𝑓(𝑥):(Assumethataisapositiveinteger.)
𝑦 = 𝑓 𝑥 − 𝑎 Resultsinthegraphshiftingdownaunits
𝑦 = 𝑓 𝑥 + 𝑎 Resultsinthegraphshiftingupaunits
𝑦 = 𝑓 𝑥 + 𝑎 Resultsinthegraphshiftingleftaunits
𝑦 = 𝑓 𝑥 − 𝑎 Resultsinthegraphshiftingrightaunits
Reflectionsof𝑦 = 𝑓(𝑥):
𝑦 = −𝑓(𝑥) Resultsinthegraphreflectingoverthex-axis
𝑦 = 𝑓(−𝑥) Resultsinthegraphreflectingoverthey-axis
Scalingsof𝑦 = 𝑓(𝑥):
𝑦 = 𝑎𝑓(𝑥) Resultsinthegraphbecomingatimesastall
𝑦 = !!𝑓(𝑥) Resultsinthegraphbecoming!
!timesastall
𝑦 = 𝑓(𝑎𝑥) Resultsinthegraphbecoming!!timesaswide
𝑦 = 𝑓1𝑎 𝑥 Resultsinthegraphbecomingatimesaswide
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434
Name: Date:
3
PracticeProblems:DotheseproblemsWITHOUTYOURCALCULATORasyouwillnothavethattoolwhenyoutakethequiz.Directions:Eachdescriptionorgraphrepresentsadifferenttransformationorcombinationoftransformationsofsome“parent”function.Fillinthemissinginformation
1. Equation:
Description:Thegraphof𝑦 = 𝑥isshiftedup2andis!
!aswide.
Graph:
2. Equation:𝑦 = − !!𝑥! + 3
Description:
Graph:
3. Equation:
Description:Thegraphof𝑦 = 𝑥!ismadetwiceastallandisreflectedoverthey-axis.
Graph:
4. Equation:𝑦 = −4 𝑥 − 4
Description:
Graph:
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434
Name: Date:
4
5. Equation:𝑦 = − 4𝑥
Description:
Graph:
6. Equation:
Description:Thegraphof2!isreflectedoverthey-axisandshifteddown5units.
Graph:
7. Equation:𝑦 = − !!!!
+ 2
Description:
Graph:
8. Equation:
Description:Thegraphof𝑦 = 𝑥 ismadetwiceastallandshiftedleft4units.
Graph:
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434
Name: Date:
5
Directions:Eachofthefollowingfiguresisoneofthebasicgraphswithoneormoretransformationperformedonit.Foreachone,
a. Identifytheparentfunction.b. Describeinwritingthetransformation(s)thatwas/wereperformed.c. Writeanequationforthenewfunction.
9.
a.b.c.
10.
a.b.c.
11.
a.b.c.
12.
a.b.c.
–5 5
8
6
4
2
–2
–5 5
8
6
4
2
–2
–5 5
4
2
–2
–4
–6
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434
Name: Date:
6
a. Identifytheparentfunction.b. Describeinwritingthetransformation(s)thatwas/wereperformed.
Writeanequationforthenewfunction.
13.
a.b.c.
14.
a.b.c.
15.
a.b.c.
16.
a.b.c.
–5 5
2
–2
–4
–6
–8
–5 5
6
4
2
–2
–4
–5 5
4
2
–2
–4
–6
–5 5
6
4
2
–2
–4
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434
Name: Date:
7
Directions:Writeaquadraticequationforeachdescriptionbelow.Showallofyourwork!17.Aquadraticfunctionthathasx-interceptsof6and−2anday-interceptof−4.18.Aquadraticfunctionthathasx-interceptsof5and–9andpassesthroughthepoint(−3,90).19.Aquadraticfunctionthathasavertexof(5,−1)anday-interceptof9.20.Aquadraticfunctionthathasavertexof(6,2)andpassesthroughthepoint(5,−2).
Math 2B/3A
Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434
Name: Date:
8
FunctionTransformationsQuizAnswerKey
1.𝑦 = 3𝑥 + 2
2.Thegraphisreflectedoverthex-axis,isshiftedup3unitsandishalfastall.
3.𝑦 = 2(−𝑥)!
4.Thegraphisreflectedoverthex-axis,shifted4totherightandmade4timesastall.
5.Thegraphisreflectedoverthex-axisandmade!
!
aswide.
6.𝑦 = 2!! − 5
7.Thegraphisreflectedoverthex-axisandshiftedright3andup2
8.𝑦 = 2 𝑥 + 4
9.a.𝑦 = 𝑥b.thegraphisshiftedleftthreeunitsandistwiceastall.c.𝑦 = 2 𝑥 + 3
10.a.𝑦 = 𝑥!b.Thegraphis3timesaswide(orthegraphis!
!as
tall)andisshiftedup3units.
c.𝑦 = !!𝑥
!+ 3or
𝑦 = !!𝑥! + 3
11.a.𝑦 = 𝑥!b.Thegraphisshiftedup4,reflectedoverthex-axisandmade1/2astall.c.𝑦 = − !
!𝑥! + 4
12.a.𝑦 = !
!
b.Thegraphisshifteddown3andleft6.c.𝑦 = !
!!!− 3
13.a.𝑦 = 𝑥!b.Thegraphisshifteddown4andistwiceastall.c.𝑦 = 2𝑥! − 4
14.a.𝑦 = 2!b.thegraphisreflectedacrossthex-axisandisshiftedright5c.𝑦 = −2!!!
15.a.y=xb.thegraphisreflectedoverthey-axis,shifteddown5unitsandmadetwiceastall(orhalfaswide)c.𝑦 = 2𝑥 − 5
16.a.𝑦 = 𝑥 b.thegraphisshiftedright2andis!
!astall.
c.𝑦 = !!𝑥 − 2
17.𝑦 = !!𝑥 − 6 (𝑥 + 2) 18.𝑦 = −2(𝑥 − 5)(𝑥 + 9) 19.𝑦 = !
!(𝑥 − 5)! − 1 20.𝑦 = −4(𝑥 − 6)! + 2
–5 5
6
4
2
–2
–4
–5 5
6
4
2
–2
–4
–5 5
6
4
2
–2
–4
–6
10 –5 5
8
6
4
2
–2
–4
–6
–8
s x( ) = – 4· x – 4
5
2
–2
–4
–6
5 5
2
–2
–4
–6–5 5 10
6
4
2
–2
–4
