2'7 Study Guide and lntervention - Mrs Browne's Algebra ...brownealgebra.weebly.com/.../2/...7_hw_and_answers.pdf2'7 Study Guide and lntervention P arent F u nctions and T ransformations

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2'7 Study Guide and lnterventionP arent F u nctions and T ransformations

Pafent GraphS The parent graph, whicl'r is the g.up\ of the parent_function,is the simplest of the griphs in a family. Each graph in a family of graphs hassimilar characteristics.

..sffiIdentifythety1reoffunctionrepresentedbyeachgraph.

The graph is a diagonal line. The graph The graph is a parabolic curve. The

"*pr"runtr an identity function. graph represents a quadratic function.

Erercises

Identifu the tylre of function repreaented by each graph.

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Name Characteristics Parent Function

Constant Function Straight horizontal line y = a,whete a is a real number

ldentily Function Straight diagonal line Y:x

Absolute Value FunctionDiagonal lines shaped

like a VY=lxl

Quadratic Function Curved like a parabola Y:x2

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Chapter 2 Glencoe Algebra 2

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2-T Study Guide and lntervention kontinued.)

P arent F u nctions and T ransformationsTfanSfofmatiOnS Transformations of a parent graph may appear in a different location,may flip over an axis, or may appear to have been stretched or compressed.

ryDescribethereflectioniny=-|r|.Thengraphthefunction.The graph ofy = *lrlis a reflection ofthe graph ofy - lrlin the r-axis.

1 v = l,lfT'-r-rrr*T' lv= lxl-nr-r2

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Exercises

Describe the translation in each function. Then graph the function.

2.y: lr + 5l 3.Y =x2-Bl'Y:x-4

Describe the dilation in each function. Then graph the function.

4.y:5x 5. y = lrlxl 6-y : ?*'

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Chapter 2 44 Glencoe Algebra 2

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2'7 Skills PracticeP arent F u nctions and T ransformation

Identify the type of function represented by each graph.

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Deseribe the translation in each equation. Then graph the function.

3.y= l*l-2 4.y:(*+1)2

5.Y = -x

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Describe the reflection in each equation. Then graph the function.

6.y = -lxl

Biology A biologist plotted the data from hislatest experiment and found that the graph ofhis data looked like this graph.What type offunction relates the variables in the experiment?

Chapter 2 45 Glencoe Algebra 2

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2-T Practice

P arent F u nctions and T ranstormationsDescribe the translation in each funetion. Then graph the function.l.y:r+3 2.y=x2-3

Describe the reflection in each function.Ihen graph the function.3. y : (-x)2 4.y = -(3)

Describe the dilation5. y = lf.xl

in each function. Then graph the function.6.4y : x'

7. CHEMISTRY A scientist tested how fast a chemical reaction occurred at differenttemperatures. The data made this graph. What type of function shows the relation oftemperature and speed of the chemical reaction?

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Chapter 2 46 Glencoe Algebra 2

l-6 Graphing Cakulator AdivityTransformalions.' Greatesl lnteger Function

A graphing calculator cm be used to display transfomations to the greatestinteger function. This is done by using the int( commmd under the MATTI:NUM mmu. ffien graphing the greatest iateger function, it is imporimt toset the calculator to Dot mode.

Graphflr) = [s! andgk) = [rl + 2 on the same areoEvaluate each fuaction forr - 0.0,r = I,x =1,8,r =2,s = -0.6,udr = -1.1. Cmpare the graphs of the function*Enterflr) in Yl mdgk) in Y2. Gmph the functions.

Keystrokes: tr lMATri E 5 Fr$l n mn F,rATHl E 5

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Use TRACD to waiuate each function for the given values.

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Keystrokes: @ 0.6 FER'I 1 lcl'T€n'l 1.3 lFlTER-l 2 Gr\rr€nl E 0.5

llNT€n] E L1 I6TEE B 0.6 linrenl I Fffi-ml 1.9 l*'rrsnl 2 ENTERI E0.SiENrEBl E 1.1 [B{rEn.l.

fl0.6) = 0, fl 1) = t, fl1.3) = I, ffz) = 2,

^-0.5) = -1, md^-1.1) = -2 I

e(0.6) = 2,e(1) = 3,e(7.3) = 3,dzt' = a,e(-0.5) = -1, mde(-1.1) = 0

The graph of 6(r) = [a + 2] is the sme m the graph of flr) = [t] shifted 2 units up.

ErsrclsecGraph each function, Dvalwto it for r = lt r = 1.8, md r = 2.Compm the graph ofthe tunction to the graph offlr) = [rl.1. g(r) = [r] - 3 2. g(r) = [r - 2] 3, g(r) = [r +

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-2.7 Study Guide and lntervention

Parent Functions and TranstormatiansPafent GfaphS the pmlt gfapb, which ie the graph of the parent function,is the simplwt of the graphs in a family. Each graph in a fmily of graphs hassimila dlaract€ristics.

'f*4{Twqry ldentify the typ€ of fuaction repruented by each graph,

The graph is a diagonal line. lhe graphrepresents m iilentity fimction.

the graph is a p*abolic we. thegraph represents a quadratic fmction.

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Exerisee

Identify the type offuaction

[4r,4.4&+ 1 by[-C1, Ell&t 1 l-L7,4.4rd:1by[{l, $llsl1 [{,7,4.4sdr 1 by [{l, Cll *J:1

stl) = -2,s(l3) = -a s(2) s -1 s(1) = -1, gfl .3) = -1, o(2) = 0 s(l) = s, g(1.3) = s,dz) = 6shifM dom 3 mitt thiied 4lht 2 unlts shitt€d lelt 4 unit3

a. 6(r) = [-r] 6.6(r) = [&] 6. e(e) = 3[sn

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s(0 = -1, g(1.3) = -e s{2) = -2 9(1) = 2, s(t3) * 2, s(2) E 4

Ell€cted dcffi lhe y.db mpcas€d by * hdinidty

t-d7, *4 rd: 1 by l-31, a1l r* t

s(1) = 3, s(1.3) s 3, s(2) = 6

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Consbd Fundion Straight horizontal lin€ y = 8, whore a is a rgal nlmbsr

ldenlity Function Straight diagonal line v

Absolul€ Value FunciionDlsgonal lin€s shapgdIike a V

Quad€lic Functon Curydd lik€ a pa€bola

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Parent Functions and Trcnslormations

2-7 Skills Practlce

Parent Functions and Transformation

Transformation9 Tlmfomations of a puent graph may appeu ia a diferent lcation,mav llip wer an uis, or may appeil to bave ben stretched or compremed,

11+::T*T'r' Demribe the reflstim in tThe graph ofy = - lr I is a reflection ofthe graph ofy = lr I in the r-uis.

= -lsl, Then gnph the tunction.

Iinear or identity quadtatic

Desibe the tmalation in emh equation" Then grtph the fuctim.

Erelrlces

Desibe the tf,&nslation in emh function. Then graph the func'tion.

1.y=x-4 2,y=lx+51 3.! =x2-3

translated down 2 units translated left I unit

Desibe the reflection in eeh eqution Then graph the furctim,

translation of thegraphofy=x4 unit6 down

translation ot thegrapholy=;v15 unils left

translation of thegraphofy=t'3 units down

Demibe the dilation in each function. then graph lho ftrnction'

4.Y = 5x a,y =|trt 6'Y =a'

rellected in the x-axis reflected in the x-axis

vertical stretcholY=1

Chapior 2

verlicalcompression vefticalstretcholy=lxl oll=x2

7. Biology A biologist plotteel the tlata from hislatest experiment mil fomd that the graph ofhis data looked like this graph. What Wpe offuction relates the vuiables in the exp€riment?

quadratic

3.r= lrl-2 4.y=(r+lY

6'Y = -x 6,y = -111

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Copyright @ Glenco€/Mccraw-Hill, a division ol The McGraw-Hill Companies, lnc.

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1.7 Pradice

Parent Functions and lransformationsDe*ribe the trmslatioa in ereh function. Tben graph tbe function.

l.y=r+8 2.y=r"-3

2-7 Word Problcm Pndi(eParent Functions and Transformations

1. GAMES Petlro decideil tn measue howclose to a trget he md his frienrls couldthrow a football. They couteal 1 pohtfor each foot away from the tilget thatthe fmtball lmcled.lhe graph of pointsvemu distmm thrown is shown here.What type of finction had Pedrc and hisfriends follwed?

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2,ASTRONOMY 'lhe graph shows thevelocity ofthe space probe Cassini a itpwsed Satum. What typ€ of fuctionbest models Cmsini's velocity?

4. BUSINESS Maria earu m howly wageof $ L0. She drew the followiq graph toshow the relation ofher income m afunction ofthe houm she works. How&d she modi& the idmtity function tocreate her graph?

translated 3 units up translated 3 units down

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I*Ilercribe the refletim in each function. Then graph the function.

a.Y - -(3)flT-fqr-rtrnffitJ -2 lol 2 | IttFI]TTTI]]IH++.H+frreflected in the x axis

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She stretched it vertically by afactor of 10.

6, HOBBIES Laua lauched a modelrmket into tle air. the heigbt ofherrocket wer time is shown by the graph.

Describe the dilation in each function. Thm graph the ftrnctim6,y =l?al 6,4s =x"

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3. GEOMETRY Chen made this graph toshow how the perimeter ofa squaechmges m the lengtl of one side igincerued. lhe original graph showedan identity fuction. Hw hm itben tlilated?

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* What type offunstion do6 thegraph show?quadratic

b, In which mis hm tle functionbeen reflected?

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e, Which directions has the graph beentrmslated? How mmy units?right 25 units andup 8l units

d. What is the equation for the weshown on the graph?

y=-(x-50F+81

7, CHEMISTRY A scientist tegled hw fast a clemical reaction occmed at differenttemperatms. the data made this graph. What type of function shows t&e relation oftemperatue md speecl of the chemical reagtion? l0

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