ry"t tqt5ry1*@,c,\,1) iteT;f

s1z Re'Rr.rus nNo Furucrro^rs rrr<f < r . " {r:,r:J.i"f;"rri",,t ?,r1to,,41. Which of the following ordered pairs is itor irn eiement of the gi

(1) (8,8) Q) (236',2) (3) (-3'6' -3) (4) (-4'6' -s)

+2. Wt i.n of the following is nor a function?

(1) thelinev: ;; -'4 (2) theparabola'r': -rt - 3x

(3) the line v : Z (4) the circle rr + vr : 16

i3 f* * 43-48: a' Graph each given function for the domain -3 = 'r< 3. b. Using this domain, s1

range of the function'i:l 'i, i a3. y : ixl

46. f(.r) : ]x + 2l

49. f(-r) : [.r]

ur. n : [i.4

44. f(.r) : 13xl

47. y:3 - ltl

50.

53.

45. -y:lxl +z(:t8,)ri"l:x+lxlf.n't,0 LWeb3

domain0<r<6. b'U|n49: 54'ineachcase:a.Graphthegivenfunctionforthe

domain, state the range of the function'

1':[.t-21nr'r : [i 'l

A1t p ! i c at itt tt s tt' ith F unct io tts

51. g(x) : i3 - xl

54. y: -r - [-r]

55. A newspaper deliverer earns $0'07 ior each paper clelivered' Thus' the earnings E is a function

nurnber n of newspapers delivered, or E : ii,ri The fbrmula to cletermine the deliverer's earni

E : 0.0'/ n, or f(n) : 0.0Jn.

a. How much is "o.n"J*n"n

20 papers are delivered'J In other words. lind f(20)'

r- E:-,r f,'r 5\ c. Find f(32). d' Find l(57)'b. Find f( l5). c' rlno r\J'l'

rs does she deliver each

.. tf l"nnit"r earns $2'66 for a daiiy delivery' how many newspapel

I

i

x

i

'II

I

Irili

56. The accompanying table shows the 8%.sales taxes to be collected

on amounts from $0'01 to $l '06' On'sales over

$ 1 .06, the tax is computecl by multiplying the amount of sale

by 0.08, ancl rounding to the nearest.whole cent'

The sales '^^,

i ii a function of the amount A of the sale'

thatis.t:f(.4^).a. Find the sales tax on an item costing 50'52: that is' find

($0.s2).Find f($0.89). c' Find f($0'39)'

Find f($0.08)' e' Find f($9'95)'

True orFalse: Sales tax is an example of a step function'

True or False'. For amounts less than $ 1'00' the tax in the

.f,^n i, equal to 87o of the amount' rounded to the nearest

whole cent.

b.

d.f.a

$0.01 to $0.100.il to 0.1-l

0.18 to 0.29

0.30 to 0.42

0.43 to 0.54

0.55 to 0.6'7

0.68 to 0.79

0.80 to 0920.93 to 1.06

l

IYntY..int;

ffi

556 Reurtotls ANo Fut,tclor'rs

(l) 1, : l5rl

i9. f(x) : 4x * l')

8. {(2,2), (3, 1), (1,3)} 9. Itz,4), (3, 1). q1. i,,,10. Draw a graph antl label the axes to represent the ftrllowine siLr:., "'..

took off and ciirrilred quickly at a constant rate to irs cruising ai.:: _ ::this altitude tbrt somc time, then dsscended slowll to iand at thc : ; r.:

its schedLrle. Conpare lhe plane's altitude to tine ttrat elapsed.11. Ii ttre fnncLion f(r) : .r2 * 4,r. find the value of tl-"11.12. Ilg(;x) : V;, fincl g(-'8).

In l3-15, in each case. select the numeruL preceding lhe expressiirrpletes the $eutence or answers fte qr_restion.

*{*@Wrrich of the following is wt afirnction'/

12t 1,: 5xl (3) v:514. The domajn for h(;r) :2x - i is -2 s.rc s J. The range is

(l) *3<.1'"<'l (2) -ll=:-y<-3(3) *lls.y<3 (4) --ll'<y<ll

15. The domain fbr p(x) * 6 * 2x is {xl*5 s .r s 1}. The greatest ,,,ai,;: :;

lange ls

(l) 16 (2) I /1\ -a

In 16-1 8, in each case, stare the largest possible domain such thar r:*, - jtiorr is a lunction.

16. fi.r) : i," ;g,

17. r-:>.r

2 t- 4-r18. r,: -i-'\:-r

In l9-21, for each given function: a. State the domain. b. State lhe -=

b.d.

+"'i'- ... .* --

I

Itt * -*",IiI

.,t/

22. Let m(x) : 5.u and d(.r) : .t - 4.a. l"incl (m " d)i6).c. Write the rule fbr (m . dX"r).

23. 4f * v;:425. l-r1 -4

71 r,: \ r - z

Find (d " rrr)(6).Write the r:ule for (d o *: ,;.;;

g20. x:; p1

+)kt 23-26: a. klenrify fhe graph of each of the foliowing as a cir.cle. ;r I

hyperbola, or a parabola. b. Sketch the graph.

24. Y "" x?' -' 426,i:4-x:)

12-11 Composition of Functions 547

3.|,forthegivenfunctionsf(x)andg(-r),find,ineachcase,theruleofthecomposition(f"g)(x).

--6x;g@):x-2=x;g@):2x-1 5

= )x,; g(x) = 5r

=L* - 3; g(x): 4r

=f;g(x):x-5 ' (f " fXx) isf(x) = x + 8, then the rule of the composttton

,-+R (2)x+16 (3)2x+8- (4)2x+16x-l-8 l'4J rr rLr

:r, I U* 5, what is the rule of the composition (g ' g)(r)?

, let h(x) : x' r 2x, andg(x) : x - 3' ln 4044' evaluate each composition'

41. (h " gX3) 42' (h " gX2)

zt5. FinJthe rule of the function (h " gXx)'

f(;) : x + 5, g(x) : 2x,andh(x) : x - 2'

ti"6l : (r " gi(t)' find the rule of the funct:n I(jJ:

i il;;. *t" "i'tii' s) 'hXx)' that is' the rule of ((k) " h)(;r)

l iitt"l = (s . hXx), find the rule of the function l(]] , ,,, .

1;;;" ,.ir" or'ti' (g ' h))(x), that is' the rule of (f " (r)X;r)'

igring parts b uno a, ,ruiJ'*rr"rrr* *'"* \(f ' s) 'h)(x) : (f " (g'h)Xx)' If yes' tell what group

ptoplny is demonstrated' lf no' explain why'

7-58, letb(x): ixl, a(x): txl, f(x):1' g(t) = x - 3' andh(r) - 2x' Find theruleof each

29. f(rt:x-l0lgtxl=4x31. f(;):x-3;g(x):x-533. f(-r) : 3x * 2; g(x): x - 3

+6 35' f(x)-5-x;g(r):xt2

"p{?{.}}*;*;"-J& rtr, : 4 - r: g(x) : x - 2

43. (h " s)(l )

" gx4)

'g)(-2)

)srtlon.

" b)(x) 43. (d ' gXx) 49' (b " gXx) 50' (g ' dXx)

i" 0(r) 52. (h " g)(x) 53' (f ' G ' n)xt) 54' (d " (h " 0Xx)

i" Gr " u))(x) 56. ib " it'tt)xt) 57' (f " t' ir)(x) 58' (f ' h " 0(x)

'..

b flno tt. 670 salestax on any item sold in her store, Ms' Reres programmed her cash register

i. . .1. The first function, s(x)' multiplies the total price of the purchases, x,I perform two tunctlon

11".il'Hl;,:1X;':t:r;;:fi#;ffi""i1", r(.r), rounds the tax to the nearest cent' that

(x):ff.' Evaluate (r's)($1'39)' b' Evaluate (r'.sX$16'79)'

.Canthe6Tosalestaxtobepaidonapurchas"ofxdollarsbefoundusing(r's)(x)?; If i(x) = x, evaluate i($1'39) + (r " s)($l'39)'

, Evaluate i($16.79) + (r' sX$16'79)'

: i, *, ;:rilll;"i'"*".,"1 paid by a cusromer for an item priced at -r dollars, does

c(x):i(x)+(r's)(x)?

ri

tiI

rl

I

/

504 BEmrrorus erun Furucrrous

ln'7-12, in each case the rule thal defines tunction g is givcn.a. Find g(3). b. Find e(^ tl.

7. s(.{) : iI 8.

10. g(,r) : x'+ x ll.

Ln 13-17 , f unctjon h is clelined by h(x)

13. h(4) 14. h(-4)

g(,t):8-x 9,

9(-r) : -'*2 t2.

,.2 _ ..- -l-,t. Fincl esch value.

ts. h(2) 16. h(1)

s(xt:r--.I--

g{x)="r2*j..'.

17. $'

In 18*22. function k is defineci by k(r) : Fi Fincl each value.

18. k(2) 19. k(e) 20. k(0) 21. k(6)

ln 23--18, use the fbllowing luncrions rn. p, and r:

mp"fx---^->2x r--j--->rr x------+x 1- 2

23. Find m(3) 24. Find p(,1I 25. Find r(3).

26. Under whic"h function (ra. p, or r) will 5 rnap to 7?

27. lJnder which function (m, p, or r) will the image of ] ne t 'l

28. Of functions m, p, and r. which ones assign 2 in the clomain to 4 in the range'?

29. The gi'aph of functir.n f consi sts of the irnion of ibur linesegments. zrs shown at the riglrt.a. Find f( - l)c. Find f(1).

e. rrnor(j).

h. Find f{0).d. Find (2).

I nincr r(zi)g. State the donain ol'lnnction f.h. State the range ol tunction l.

e. Finri *(t i) f. Fincl ,(-t i)g. For what value(s) of .r will eQ) : 2\?

@) Smrc the clomain of tunction g.

QState the range of function g.

Ex. 29

)The graph of functitin g is shown at the right.

@rino s(- l). b. Find grl).

Q)Find g(2). d. Find g(0).") 7c)-_ a.)?(^)*lt h ,2'r3x<

4%;/t:v*

i:-t-' j

-* 'i-

i\i

,3i

47'J

10-9 Dividing Radicals with the $ame tndex 415

i,ir 15*36, raise each e,rpression to the indicatecl pr:wer, ancl simpliiy the resr.rlt.

/t,rq i !'12

. ;:t:1G;3 34. t4 + \r5): 3s. (j - \.'2)r

-f:r: 17-48. two irrational nutrrbcrs are given. a. Find tlre procluct

Suie ivhether. the proiluct is rational r.lr irrational.

za. f] r,'a)'

32. (f'e)l

36. {1 - r,t)'of tlre n';rribers in sinrplest l-onn.

3e. i vt. lo\,'it42. 3\'612\'i' - r.'1,1r

4s. (5 i. \,T0x5 - vjo)48. {2 * \:1x2 + \.t)

26. (2\,'n):

J0. i4V!)r

27. (3\,'7):

il. t tt?)3

sr "i. :rz5

; \ 10'4j;.:-vTiixs+ v.'i0t

:\,i*lx\4+l).ri;rr;t -52. express the area of each

3s. 8v€.lvtat tfigVn - ii)44. e + v"To)(s-Vto)

47. (z + VgXl - r/Itfigr"rre in simplesr frtril.

.':.iir ,til

,.:::+- iil::.:,i-X

:''ill$,rLi$!r

'iliii,iir4:i

r{fi

' ,il

r#

-ll::j)

::,]'ir(

r:::::il I

,;ii:::3

,itL

::;({':.

lr:-+

i::i.,

:: jsl:t!

::ti

:r'li,:ll

::..i.'$::ft

;

iiI;K

I,::1

1i

i9::.lJ

Llil

-r:3+

q) .,G

pressed:

rtt$kl the value of .r.,: * 4;r * I rvhen:

b. x: V3 c. r - I l- \/-) =i5;l

s0. u---t] fi N"7i l* l\:'F- - V+-sl \VTs tr \

I ri7.T:

'.';* hase ancl the height of a parirllelograrn uteasure 3\.7 centirnetcls and 2V'lJiti*r-".F.ctively. Find thc numherr of squire centilneter$ in the area of the parallelogranr.* rn .sirnplest radical fonn b. as a raiional rnuuber correct to the r?€'drc,rt tenth.#1,s; ihe value of'x' -- 4 when

;. ^t;S,.i - V-1

b. x: \4e",r:{i-t

e.

t:

/) : ; {,*'t€

= (r_)( 4\tti{.6i

; {+k} ({ar } ". / -e\, f ,. f-'* iL, {u.iri(3}s}

3ruTNlHS RfrMTGStl$ qrylYH TEIS $A[IH INI'EX

We have learnecl thatif o olyd

h are positive rrumbers and the ildex n is a

counting nurrbel, then ;f; -"ilij U, applying the symrnerric plr:perry of equality

tci the given stafement. we form a rule to find the quotient of two radicirls withllte same index. narlcll,:

If a ancl b are positive nurnbers and the inclcx n is il. cor.rnting numbet, therr:

t,; ,,1;i.l v,