n n n n n n n n n n
s 7th Edition Hornsby n n n
Name:nn
Chapter 2 Test Form An n n n Date:nn
l. MatchnthensetndescribedninnColumnnInwithnthencorrectnintervalnnotationnfromnColumnnII.nChoicesninnColumnnIIn
maynbenusednonce,nmorenthannonce,nornnotnatnall.
ColumnnI ColumnnII
(a) domainnof fn nx nnnxnn3
2
A.n 3,nn
(b) rangenof fn nx nnnxnn3
2
B.n 0,nn
(c) domainn ofn xn n y2n n3 C.n 3,nn
(d) rangenofn xn n y2n n3 D.n ,0
(e) domainnof fn nxnn3n x E.n 3,nn
(f) rangenof fn nxn 3nnx F.n ,3
(g) domainnof fn nxn 3n xnn3 G.n ,n
(h) rangenof fn nxn 3n xnn3 H.n ,0
(i) domainnof fn nxnnn xnn3
(j) rangenof fn nxnnn xn n3
2. Thengraphnof yn n fn nxn isn shownn here.
Sketchnthengraphnofneachnofnthenfollowing.nUsenorderednpairsntonindicaten3npointsnonnthengraph.
(a) yn n fn nxnn3 (b) yn n fn nxnnn3 (c) yn n fn nx
(d) yn n nfn nx (e) yn n3nfn nxn (f) yn n fn nx
3. Ifnthenpointn 9,n 12n liesnonnthengraphnof ynn fn(x),n determinenanpointnonnthengraphnofneachnequation.
(a) n1n (b) fn 3xn
fn n x
n
9n
4. Graph yn nnfn nxnn bynhand.
1
fn(x)nnnxnn2 1 (b) fn(x)nn xnn3
2nn
(a)
2
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n n n n n n n n n n
s 7th Edition Hornsby
n n n
5. Observenthencoordinatesndisplayednatnthenbottomnofnthengivennscreennshowingnanportionnofnthengraph
yn n fn nx. Answerneachnofnthenfollowingnbasednonnyournobservation.
(a) Ifnthengraphnisnsymmetricnwithnrespectntontheny-
axis,nwhatnarenthencoordinatesnofnanothernpointnonnthengraph?
(b) Ifnthengraphnisnsymmetricnwithnrespectntonthenorigin,nwhatnarenthencoordinatesnofnanothernpointnonnthen
graph?
(c) Supposenthengraphnisnsymmetricnwithnrespectntontheny-
axis.nSketchnantypicalnviewingnwindownwithndimensionsn 5,n 5n byn 0,n 10.n Thenndrawnthengraph
nyounwouldnexpectntonseeninnthisnwindow.
6. (a)n Writenandescriptionnthatnexplainsnhownthengraphnof ynn2 xn 1 3ncannbenobtainednbyntranslatingnthe
graphnofn yn nnn x.
(b)n Sketchnbynhandnthengraphnof yn n2n xnn2n n3. Statenthendomainnandnthenrange.
7. Considernthengraphnofnthenfunctionnshownnhere.
Statentheninterval(s)novernwhichnthenfunctionnis:
(a) increasing (b)n decreasing (c)n constant (d)n continuous
(e)n Whatnisnthendomainnofnthenfunction? (f)n Whatnisnthenrangenofnthisnfunction?
8. Solveneachnofnthenfollowingnanalytically,nshowingnallnsteps.nNextngraph y1n n 4xnn2 and y2n n2n innthe
standardnviewingnwindownofnangraphingncalculator.nThennstatenhownthengraphsnsupportnyournsolutionninneachn
case.
(a) 4xnn2n n 2 (b) 4xnn2n n 2 (c) 4xnn2n n 2
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n n n n n n n n n n
s 7th Edition Hornsby n n n
Test Form 2-A (continued)
n n n Name:nn
9. Give fn nxnn3x2n n2xnn6n andn gnnxnnn3xnn5, findneachnofnthenfollowing.nSimplifynthenexpressionnwhen
possible.
f
fn
(a)n nfn n gnnxn (b) nx (c)n thendomainnofn
g g
f nxnnhnn fn nxn
nfn ngnnxn hn n 0
n n
(d)n (e)
h
x 2nn6nnnnifnnxnn1
10. Considernthenpiecewise-definednfunctionndefinednby fn nxnn .
x ifn xnn1
(a) Graphn fn bynhand.
(b) Usenangraphingncalculatorntonobtainnannaccuratengraphninnthenwindown 5,n 10n byn 10,n 10.
11. Then pricen ofn postagen forn mailn isn definedn byn then functionn P(nx)n n 0.49xnn1,n wheren xn representsn then weightn onfthenle
tterninnounces.
(a) Usingndotnmodenandnthenwindown 0,n 5n byn 0,n 4,n graphnthisnfunctionnonnangraphingncalculator.
(b) Usenthengraphntonfindnthenpricenofnan2.42nouncenenvelope.
12. ThenmembersnofnthenNewnJazznbandnwantntonrecordnannewnCD.nThencostntonrecordnanCDnisn$4000nfornstudion
feesnplusn$1.50nforneachnCDnproduced.
(a) WritenancostnfunctionnC,nwheren xn representsnthennumbernofnCD’snproduced.
(b) Findnthenrevenuenfunctionn R,n ifneachnCDninnpartn(a)nsellsnforn$12.
(c) Writenthenprofitnfunction.
(d) HownmanynCD’snmustnbenproducednandnsoldnbeforenthenbandnearnsnanprofit?
(e) Supportnthenresultsnofnpartn(d)ngraphically.
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