17, r) -,r I -l19.t... 121.2t-314 23. ^t -rr - .docx

17, r) -,r I : -l
19.t:...: 1
21.2t-31:4
/ 23. ^t: -rr - 1)t I,r r.= ll-vl
11 1
Evaluating a Function In Exercises 29-14, evaluate the
function at each specified value of the independent
variable and simplify.
29.fO-3t+t
(a) f(2) (b) /(-4) (c) f(r + 2)
30. s(y) :1 - 3y
(a) s(o) tul s(l) (c) s(s + 2)
tlzt.t(t):t2-2t
(a) h(.2) ft) /,(1.s) (c) h(x + 2)
32. v(r) - !rr3
(a) v(3) (b) Y(;) k) v(2r)
33./(.-r)::-./y
@) f(a) (u) l(0.2s) (c') [email protected])
3a.f(x)- aE+8+2
(a) f (-+) (b) /(8)
1
' x'-9

(a) q(-3) (b) q(z)
)t2+
36. ./(r)- t'
(il qQ) 0) q(o)
lrl
37. i(r) : "'x
ar f(e) (b) /(-e)
38. -.,. : -r *4
: , -i (b) /(_5)
-, - l. x<0
'lq -, - l. .r > 0'-
'-
6r t(0)
', - -:. -r < 0t.
> |
1..
1OG Chapter I Functjons and Their Graphs
Testing for Functions Represented Algebraically In
Exercises 77-28. determine whether the equation
represents,r' as a function of r.
18.x:]2+1
20. y :-lf+ 5
22.r:-.y+5
24.r'l!2:3
20. lyl :1-x

28.r,:8
(c) /(x - 8)
(c) q(y + 3)
(.c) q(.- x)
(c) /(t)
(c) f(t)
(c) JQ)
,cl .f(l)
Evalr.rating a Fr.lnction In Exercises 45-48, assume that
the domain of/is the setA = {-2, - 1, 0, 1, 2}. Determine
the set of ordered pairs representing the function/.
[.rr-4. x<o42.fG)-1r_r,., r>0L1 - i.
(il f?2) (b) /(0)
[.r- ]. t<0
I
a3.f(x)-1a. 0<r<2
L*, + t. r > 2
(a) .f(.-2) (b) /(1)
(s - ), r < otJ
44. ffrr --]s. us r < I
l.+*- r, r2 l
(a) J(. 2) (b) /(])

(c) /(1)
@ f(a)
(c) f(t)
a6. .f(.x) : x2 - 3
as. /(x) : lx + 1l
45. f(x) - x2
a7. f(x): lxl + z
Evaluating a Function In Exercises 49 and 50, complete
the tahle.
4s. h(t): llr + :l
l" - ?l50..f(r) -:
Finding the lnputs That Have Outputs of Zers In
Exercises 51-54, find all values of x such that/(r) = g'
st. 16) : 15 - 3x 52. f(x): 5r * I
3r-4
sa. f(x') - 2r-3s3. /(x) :
Finding the Dornain of a Function In Exercises 55-6J.
find the domain of the function.
,l ss. fG): 5x2 + 2x - | s6. s(ir) : 7 - 2x2
4-3v
57. hhl - ' 58. ,s( r') -I y-)
se. /(x) - 1C - 1 60. /(x) : X/" + 3x

. t 3 l0
{ el. gtrt - ' - 62. h(r) - .., 1..I f t- i LA
r'*2 -,8+6
64./(:r) :--' o f .t
t -5 -4 -3 -1
It(r)
,t 0 l2
I
2
4
/(')
63. s(.v) : 5- 10
the Domain and Range of a Function In 1)
mriffs 65-68, use a graphing utility to graph the
hhu Find the domain and range of the function.
. ,.-
-E' -
+ i 66. f(x): 1F I 1
68. g(x) : I, - sl.j1- -r,-; : i1r + 3l
I. Geometry Write the areaA of a circle as a function of
rs --ircumference C.
il" Cmmetry Write the arca A of an equilaterai tiangle

"ts i tunction of the length s of its sides.
1!- E4loration An open box of maximum volume is to
s made from a square piece of mateial, 24 centimeters
cm a side, by cutting equal squares from the corners and
uuia-e up the sides (see figure).
,"1 , The table shows the volume 7 (in cubic centimeters)
of the box for various heights x (in centimeters).
L-se the table to estimate the maximum volume.
i Plot the points (x, I/) from the table in part (a). Does
rtre relation defined by the ordered pairs represent V
a-s a function of x?
; ff tr'is a function ofx. write the function and deterrnine
ir-' domain.
; L -'.- a graphing utility to plot the points from the
::ile in part (a) with the function from part (c).
FL.m'closely does the function represent the data?
Erpiain.
Section 1.3 Functions 107
Geometry A right triangle is formed in the first
quadrant by the x- and y-axes and a line through the
point (2, 1) (see figure). Write the area A of the triangle
as a function of x, and determine the domain of the
function.
-I
Geometry A rectangle is bounded by the x-axis and
the semicircle y - -66 - *'(see figure). Write the
areaA of the rectangle as a function of -x, and determine

the domain of the function.
74. Geometry A rectangular package to be sent by the
U.S. Posta] Service can have a maximum combined
length and girth (perimeter of a cross section) of
108 inches (see figure).
Write the volume V of the package as a function of
x. What is the domain of the function?
Use a graphing utility to graph the function. Be sure
to use an appropriate viewing window.
What dimensions will maximize the volume of the
package? Explain.
73.
(a)
(b)
(c)
1
2
3
4
5
6

484
800
972
1024
980
864
x +24-2x- x
-6 4
krcreasing and Decreasing Functions In Exercises
5-26, determine the open intervals on which the
hnction is increasing, decreasing, or constant.
Section 1.4 Graphs of Functions 1 1 9
ae. f(x): [, - 1n + 2 s0. /(x) : [, - 2l +
sl. /(x) : [2,] s2. f(t) : [4xn
Describing a Step Function In Exercises 53 and 54, use
a graphing utility to graph the function. State the
domain and range of the function. Describe the pattern
of the graph.
53. s(x) :2Ex - ll+rll)tr+ x/
sa. s(x) : z(1* - [*,n)'
Sketching a Piecewise-Defined Function In Exercises
55-62, sketch the graph of the piecewise-defined function
by hand.

lI. -r-r + !2 : 25
6
x" .f(") :1*
5./(r):x3-3xz+2
4
4
!7. f(x) : 3
fi. f(*) : x2/3
3r. /(x) -- ,'G + Z
22. x2 :2xy - 1
4
2a. f(x) : x2 - 4x
3
-5
26. f(x) : lF - 1
7
{ ss. f(*):{?. * ''
LJ-X.
lx + 6.
56. l(*) :
lz* _ +.
l./tri
57. llx): I-;---'
LV4 - x'

[l - t* -58./{x) :l
-j
LVx - L'
lx + 3.
I
se. f(x): j3.
[2, - t.
[x+5'
60. g(x) : l_2.
[s* - +,
fz* + t.6t..flx):1,
lx'- /'
(^
62. hx: ]', I :'
L"{- T r.
63. f(x) : s
6s. f(,*) : 3x - 2
,f el. n(x) : x2 - 4
6e. f(x) : Jl -x
7t. f(x) : lx + 2l
x<0
x>0
x<-4
x>-4
x<0
x20
i)', x<2
x>2

x<0
0<x<2
x>2
ir : -J
-3 < x < 1
x> 7
x<-7
x> 1
x<0
x>0
-4 ffi
-l
Increasing and Decreasing Functions In Exercises
v7-i4, (a) use a graphing utility to graph the function
ud (b) determine the open intervals on which the
function is increasing, decreasing, or constant.
28. f(x) - x
30. /(x) -f/q
32. f(x) : -I - ,
33. "f(r)
: l, + 1l + lx - 1l
-ta."f(r) : - lx + 4l - lx + 1l
Approximating Relative Minima and Maxima In
Frercises 35-46, use a graphing utility to graph the
function and to approximate any relative minimum or
relative maximum values of the function.

lx.f(*): x2 - 6x 36. f(x):3xz -2x- 5
ln. l,:2x3 + 3x2 - 12x 38. y: x3 - 6x2 + 15
39. lz(x) : (* - I)-/i a0. s(x) : [email protected] - *
AL f(x) : x2 - 4x - 5 a2. f(x) : 3xz - 12x
{r. /(x) : x3 - 3x a. f (x) : - x3 + 3x2
{5."f(r):3x2 -6x* I a6. f(x):8x- 4x2
t-. l-i[6ry of Parent Functions In Exercises 47-52,
dietch the graph of the function by hand. Then use a
graphing utility to verify the graph.
a7. f(r) : fixn + z a8. f(i: [,n - 3
Even and Odd Functions In Exercises 63-72, ase a
graphing utility to graph the function and determine
whether it is even, odd, or neither.
Think About lt In Exercises 73-78, find the coordinates
of a second point on the graph of a function/if the given
point is on the graph and the function is (a) even and
(b) odd.
tt. (-), +)
7s. (4,e)
77. (x, -y)
6a. f(x) : -e
66.f(x):5-3x
68. /(-r) : -x2 - 8
70. sQ):11 * |
72.f(x):-lr-51
t+. (-j, -t)
76. (s, - 1)

78. (2a,2c)
-4
120
79.f(t):t2+2t-3
./sr. g1r1 : x3 - 5x
83. /(x) : x{-P
85. s(s) : 4s2/3
87.f(x):4-x
89. /(x) : x2 - 9
93. l
,
It-L
Chapter I Functions and Their Graphs
Algebraic-Graphical-Numerical In Exercises 79_g6,
determine whether the function is even, odd, or neither
(a) algebraicallS (b) graphically by using a graphing
utility to graph the function, and (c) numerically by
using the table feature of the graphing utility to compare
/(x) and /(-x) for several values of r.
Finding the lntervals Where a Function is positive In
Exercises 87-90, graph the function and determine the
interval(s) (if any) on the real axis for which f(*) > 0.
Use a graphing utility to verify your results.
80. /(x) : .{6 - 2x2 + 3

82. h(x): 13 - 5
8a. fQ) : t,G + s
86. /(s) : !c3/2
88. /(x) : 4r t 2
90. .f(*) : x2 - 4x
an overnight package from New york to
Atlanta is $18.80 for a package weighing up
to but not including I pound and g3.50 for
each additional pound or portion of a
pound. Use the greatest integer function to
create a model for the cost C of overnight
delivery of a package weighing r pounds,
where x > 0. Sketch the graph of the function.
94. )
4
./ss. fuonELtNG DATA
The number N (in thousands) of existing condominiums
and cooperative homes sold each year from 2000
through 2008 in the United States is approximated by
the model
N : 0.482511 - t1.293t3 + 65.26t2 - 48.9/ + 578,
0<t<8
where / represents the yeal with t : 0 corresponding
to 2000. (Sonrce: Narionai Association ol Realtors)
(a) Use a graphing utility to graph the model over the
appropriate domain.
(b) Use the graph from part (a) to determine during
which years the number of cooperative homes and
condos was increasing. During which years was

the number decreasing?
(c) Approximate the maximum number of cooperative
homes and condos sold from 2000 through 200g.
96. Mechanical Engineering The intake pipe of a
lO0-gallon tank has a flow rate of 10 gallons per minute,
and two drain pipes have a flow rate of 5 gallons per
minute each. The graph shows the volume V of fluid in
the tank as a function of time /. Determine in which
pipes the fluid is flowing in specific subintervals of the
one-hour interval of time shown on the graph. (There
are many correct answers.)
10 20 30 40 50 60
Time (in minutes)
E
e
g
91. Business The cost ofusing a telephone calling card is
$1.05 for the first minute and $0.08 fbr each additional
minute or portion of a minute.
(a) A customer needs a model for the cost C of using
the calling card for a call lasting / minutes. Which
of the following is the appropriate model?
Cr(t):1'0s+0.08[/-1n
czo : 1.0s - 0.08[-(/ - l)n
(b) Use a graphing urility ro graph the appropriare

model. Estimate the cost of a call lasting lg minutes
and 45 seconds.
E SZ. Whyyou shoufd t's*rn it (p. t tTl The cost of sending
=
:
J Using the Graph of a Function In Exercises 93 and.94,
write the height ft of the rectangle as a function of x. r00
a0
e50
(.)
'.i ,(
t,
-i f +r - I
{60, 100)
(45, s0)
(30. 25)
Chapter I Functions and Their Graphs
Vocabulory and Concept Check
1. Name three types of rigid transformations.

2. Match the rigid transfbrmation of -r, : /(x) with the correct
representation, where c > 0.
while a reflection in the -v-axis of y : /(;r) is represented Ay
h(,x) -
4. A nonrigid transfbrmation of y : /(x) represented by cl(x) is a
vertical stretch
when
-
and a vertical shrink when
Procedures and Problem Solving
(a) /z(,r) :./(x) + c
(b) h(x) : JQ) - ,
(c) h(:r) - .f (.' - c)
(d) /z(r) : /(.t + c)
In Exercises 3 and 4, fill in the blanks.
Sketel':ing Tr*r+s$srm*tions In Exercises 5-18, sketch
the graphs of the three functions by hand on the same
rectangular coordinate system. Verify your results with a
graphing utitity.
5. r(x) : "{
s(r) :x-+
h(x) : 3,
7. f(r): 12
g(x) :x2+2
h(r')-6-2)'

e. fQ) - x2
s(x) : -*+I
h(.r) - -(x - 2)z
tt. 1Q) :
"z
s(r) : jr'
h(r) : (2x)2
13. l(x) : lxl
g(;r):l"rl -t
/z(x) : lx 3l
15. /(r) : '6
g(r) : -,G +l
h(r):.,8-z+t
I
t7. f(.r) : -
,ot:1 *z
h(x: | * 2' x- |
(i) horizontal shift c units to the left
(ii) vertical shift c units upward
(iii) horizontal shift c units to the right
(iv) vertical shift c units downward
e. [email protected]: L*
s(r) :)x+2
h(*)-ia-zl
8. /(x) : ,z
g(r):x2-4

h(*)-(x+2)2+1
10. /(-r) : (x 2)'
s(x) -(x+2)2+2
n(i: -(-r - 2)'- t
12. f(x) : x2
o("1:1r2+2+"
n(i - i*'
la. /(x) : lxl
s(r) -lx+31
h(*):-2lx+21 -1
16' JQ) - Jr
s(i : i'G
h(x):-Jx+1
I
18. l(:r) : -
x
I
s(r):- 4
.r
Sk*t*hing Tr*nsf*rnrnti*::s In Exercises 19 and 20, use
the graph oflto sketch each graph. To print an enlarged
copy of the graph, go to the website www.mcthgraphs.com.
19. (a) y-.('lx)+2
(b) v : -.f(,)
(c)v-l(r-z)
(d) r:/(x + 3)

(e) y : 2/(r)
(0 r - l(-x)
tel ., : /(i,)
20. (a) I :./(r) - 1
(b).y:l(x + 1)
(c)r:"r(,-l)
(d)y:-f(.r-2)
(e) r:l(-r')
(f y : jl("r)
tor .,: fl 1r')
J -','
(1,2)
r-l i-r
(-2,4)
f
Err*r Analysis In Exercises 21 and, 22, describe the
error in graphing the function.
21. 1(r): (r + 1)2 22. f(x) : (, - 1)'
]
.l/rz. o
rz:+
(1,0)
(0. - 1)
+-i"'---"-i
I

r,L
3. A reflection in the r-axis of y : .f(x) is represented by h(x)
x*3/,(r)
Section 1.5 Shifting, Reflecting, and Stretching Graphs 129
lx:*:.G+z
!5. .r : (* - 4)'
,F ----1-.)ir, |
-
A L
F.' g5r"r, of Parent Functions In Exercises 23-28, {+5.
onFare the graph of the function with the graph of its
prent function.
24. y:! - sx
26. y: lx + sl
28. y : -,G=a
f= tibrary of Parent Functions In Exercises 29-34,
*[email protected] the parent function and describe the
transformation
*orn in the graph. Write an equation for the graphed
fuetion.
D.530.4
-4

ltr. 5
1
ltt.
Rigid and Nenrigid Transforrnations In Exercises
*846, compare the graph of the function with the graph
dits parent function.
/35.r,:-lrl
rl" -r: (-r)2
:p.r:a
t.a. n1x) : +lxl
{3. g(x) : a1x3
as. "r(r)
: -,4;
Rigid and Nonrigid Transfcn*aticns In Exercises 47-50,
use a graphing utility to graph the three functions in the
c me yiewing window. Describe the graphs of g and h
rdative to the graph of/.
t7" f(*) : x3 - 3x2 48. .f(x) : x3 - 3x2 + 2
s(.r) : f(x + 2) s(x) : f(* - r)
h(i : +it h(x) : f(3x)
!i- 20'10/used ufder llcense fr0m Shu11-"rst0ck enm
Deseribing Transfarmations In Exercises 51-64, g is
related to one of the six parent functions on page 122. (.a)
Identify the parent function/. (b) Describe the sequence
of transformations from;f to g. (c) Sketch the graph of g
by hand. (d) Use function notation to write g in terms of

the parent function/.
s1. s(x) :2 - (x + 5)2 s2. [email protected]): -(, + 10)2 + s
53. s(x):3+2(x-4)2 sa. g(x): -iA+T2 -2
ss. s(x) : 3(x - 2)3 s6. s(x) : -j(x + t)3
s7.sG):@-t)3+2
s8. s(ir) : -(. + 3)3 - 10
f(.):x3-3x2
s(x) : -tt,)
h(*) : f(-*)
50. /(r) : x3 - 3x2 + 2
s6) : -fG)
h(x) : f(2x)
60.s(x)- f -nox- I
62.sG):+1,-21-3
6a.g(x):--/xtt-e
-8
32.
34.
1
se. s(r) : '' - e,Y-t6
61. s(x) : -21* - 1l - 4
63.sG):-i-/.+z-r
65. M*SELING DATA
The amounts of fuel F (in billions of gallons) used by
motor vehicles from 1991 through 2007 are given by
the ordered pairs of the form (t, f(t)), where r : 1

represents l99l . A model for the data is
F(t) : -0.099(t * 24.t12 + 183.4.
(Source: U.S. Federal Highway
Administration)
(1, 128.6)
(2,132.9)
(3, 137.3)
(4, 140.8)
(s, r43.8)
(6, t47.4)
(1,1s0.4)
(8, 1ss.4)
(e, t6t .4)
(10, 162.5) 0q,fiZ.S)
(11, 163.5) (1s, t14.8)
(12.168.1) (16, 175.0)
(i3, 170.0) (17, ti6.t)
(a) Describe the transformation of the parent function
[email protected]: P.
(b) Use a graphing utility to graph the model and the
data in the same viewing window.
(c) Rewrite the function so that / : 0 represents 2000.
Explain how you got your answer.

36. y - l-xl
38. v : -r:
40.v:-1
x
42. p(x) : x2
aa. y -- 2.G
+e. y: li{
A,r/ t
2
2 3
-l
Section
.l .6 Combinations of Functions 137
: : sulary dffid Ceffie€pf'CC*ee$*
.:-i:es l-4, fill in the blank(s).
,.lctions./and g can be conrbined by the arithrnetic operations of
and to create new functions.
of the function.l with the firnction g is (./. .cxr) : .l(C(-r))
: - :1i3rr1 of .1 " .C is the set of all .r in the domain of g such
that _ is in
. r.iin of.f.
:- ,r]lpoSe a composite function. look lbr an _ and an function.

: - . . S)(r) : 71r: + 1). what is g(;r)'/
: :
=
Cures and Pro&Jerm $o/wfngr
-; r-: :Lj:il *flTrav+ f*:r:r-ti*r:* In Exercises 7-10, frv"tl:-
ratiitq +r:;+.rici:r**ire {*ml;!*+qj+* *f Sr,i*:sti*ft* In
': rraphsof/andgtographh(x)= (/+g)(-r).To Exercises 19-32,
evaluate the indicated function for
' , enlargedcopyof the graph,gotothe website f(i=f -l andg(r) =x
-2algebraicalll,. Ifpossible,
- -:itqraphs.com, use a graphing utility to verify your answer.
-l- l -* -t
23
.: :, -:i*=cti< '[*r::hi::;r'*i*..r: c]f Furrcti*a:: In
.=. 11-18, find (a) (.r+c)6), (b) (/-s)G),
, . and (a) (/SXr). What is the domain ot flg?
:'-3, g(r) :.t-3
-lr-5. s(x):1 r
:,r. g(r)-1-x
.)l1l: A -./
5. g{-i)-.,/t -,
-rrr 4. s(r) :*
-1
* re ph i r:q i+ * & rit* ;-* elic il*r-s: i=i r:*ti*n *f f qJ i-.slii-
=:: :

Exercises 33-36, use a graphing utility to graph
functions.f, g, and /z in the same viewing windou..
19, (.f + s)(3)
2t. f s)(0)
zt. (fg)(6)
2s. (fls)es')
27. (f dQt)
zs. (fg)( 51)
tt. (f'lg')(-t)
20. (f .s)( 2)
22. (..f + 8x1)
za. (.fg)( 4)
26. (fls)$)
28. (.f + d(.t 4)
30. (/s)(3/)
32. (f ls)k + 2')
In
the
3
33. l(:r)
34' f(')
3s. /(-r)
36. .f(r)
38. /(-r) :
3e. /(x) :
a0. f(r) -
*r**hir:+ * lur: +i l--li:*=: In Exercises 37-40, use a
graphing utility to graph /, g, and f + g in the same
viewing windorv. l:hich function contributes most to the

magnitude of the sum when 0 < x < 2? Which function
contributes most to the magnitude of the sum when
x>6?
37. ./'(i) - 3r, s(, - - l0
: lr. g(r) :,r - 1. ft(.r) : f(r) + g(-t)
: 1-r, s(-t) : -r * 4. /z(r) : f(r) ,c(x)
g(.r) - l.r. /ir.rl-/lr) 'g{.r)
= 4 -.r2. g(rr - r. /rrr) :/rr)/g(,)
:tC
-
l.I(-r): J-r+-:
e(-r) - -3r'2 - 1
I
g(-r )
rl
I---
I
)
L-
g(r) - :r3
Chapter 'l Functions and Their Graphs

Vocobulary ond Conceqt Check
In Exercises 1-4, frll in the blank(s)'
1. If/and g are functions such that/(80)) : x and g(/(x)) : r' then
the function g is the
function ofl, and is denoted bY _-- '
2. Thedomain of/is the of-f 1, and the of/-t is the range of f,
3. The graphs of f afif 1 are reflections of each other in the line
4. Tohaveaninversefunction,afunction/mustbe-;thatis'/(a)
:[email protected] implies a: b'
5. How many times can a horizontal line intersect the graph of a
function that is one-to-one?
6. Can (1, 4) and (2, +1 Ue two ordered pairs of a one-to-one
function?
Procedures ond Problem Solving
Finding lnverse Functions lnformally In Exercises 7-14,
find the inverse function of / informally' Yerify that
.f (.f '(x)) = x and/-l( f (*)) = x.
Verifying lnverse Functions Atgebraically In Exercises
tg-iq, show that / and g are inverse functions
algebraically. Use a graphing utility to graph/ and g in
th-e same viewing window. Describe the relationship
between the graPhs.,f t. f(x) : ex
{ s.f(r):x*7
tt. f(x) : 2x + 1
13. f(r) : i,6

8. /(r) : 1x
10. l(x):x-3
12. f(x) : (x - )la
t4. f(x): xs
(b)
ldentifying Graphs of lnverse Functions In Exercises
15-18, match the graph of the function with the graph of
its inverse function. [The graphs of the inverse functions
are labeled (a), (b), (c), and (d).1
,l ts. f(*) : *', eQ) -- 1G 20. f(.) _- :, g(x) :x
21. f(t) : J* - a; s(x) : x2 + 4, x > o
22. ltrl -- 9 - 12. x > 0: g{x) : ./q - x
/ zl. tQ) : t .r'. s(r) -- { - r
x>o; s(x):? o<x<1
Algebraic-Graphical-Numerical In Exercises 25-34,
show that/andg are inverse functions (a) algebraically,
(b) graphically, and (c) numerically.
2s. f(r) : -f,, - z, s(ir) : -
2x*6
r-9
26.flxt:
^
g(x):4r-9
27. 1(xl-xj-l 5. g(x) :f r-5

zs. tQ) : i, sG) : 16
2s. fG) : -rT-, s(r) : 8 t12, x < o
30. ./(x) : 1trx - 16, s(x) :
=
Q
3t. f(r) : 2x, g(x) = !2
32..f(x):r - 5, s(r) : x + :
, x-l 5x-l
,/ ll. 1t*l:
", ,
R(r) : - r - l
r-l-l 2xl3
3{./(x) :*_, P(r)-- -- I
2a. f(r)
(a)
(d)(c)
t6.15.
7
-1
4

-4
4
-4
7
_,1
7
1
7
-1
4
I
4
4
-4
17. 18.
trar*iffingWhether Functions Have lnverses In Exercises
.G--lE. does the function haye an inyerse? Explain.
#- Dotnain Range 36. Domain Range

Section 1.7 Inverse Functions 149
Analyzing a Piecewise-Defined Function In Exercises
57 and 58, sketch the graph of the piecewise-defined
function by hand and use the graph to determine
whether an inyerse function exists.
lx'. o <.r < I
51. tlxl: <
[x. .r> 1
58. /(x) : [t- - ']t
'r < 3
l(x - 4)i. ;t' 2 3
Testing for One-to-One Functions In Exercises 59-70,
determine algebraically whether the function is one-to-
one. Verify your answer graphically. If the function is
one-to-one, find its inverse.
s9. f(x) : x4
60. s(-r) : x2 - x4
3x*4
6t. flr): _)
62. f(i: 3x * 5
1
63. f6): x'
4
64. hx): .x'

6s. .f(x): (a + 3)2,
66. q(x): (x s)',
,f ez. f(*) : J2" + 3
6s. /(x) : -C - 2
6e.fk)-lx 2 . x<2
70. f (x) : x2+1
Finding an lnverse Function Algebraically In Exercises
71-80, find the inverse function of/ algebraically. Use a
graphing utility to graph troth f and f-r in the same
viewing window. Describe the relationship between the
graphs.
,ftt.f(x):2x-3
72. f(x) -- z,
/ ts. fG) : *'
7a.f(x):x3+1
75. f(x) : x3/s
76. f(x) : x2, ,x > 0
,/tt. Itxl: J4-=. o < x < 2
78. ltx) : J16 -?. -4 -< x < 0
4
7e. f(x) : -
x
80. f(x) : 4
Jx
I can --------- $1
6 cans -------- $5

il cans
-$9
l-l cans ---..--- $16
ll2hour _>$40
lhow/-$70
2 hours -' -$720
4hottrs/
40.#.
42.
.tr. r-3, 6), (- 1, s), (0, 6)]
JL - rr. 4), (3,1), (1,2)j
fucognizing One-to-One Functions In Exercises 39-44,
&ermine whether the graph is that of a function. If so,
&termine whether the function is one-to-one.
L
Using the Horizontal LineTest In Exercises 45-56, use a
graphing utility to graph the function and use the
Horizontal Line Test to determine whether the function
b one-to-one and thus has an inverse function.
x>-3
x<5
a
{5./(.r) :3-i,
x2

x']_7
a6. f(x): lG * 2)' - t
r', -.
48. g(x) :- - .^o,r"
te. h(x): n6 -? so. /(x) : -2xJTe -7
sl. /(r) : 10 s2. f(x): -0.65
53. s(x) : (, + 5)3 54. flx) : xs - J
s5. /z(x) : lx + 4l - l, - 4l
l* 6l
lx -r ol
Chapter 2 Solving Equations and lnequalities
Vocabulary ond ConcePt Check
In Exercises 1-4, fill in the blank.
1. A(n) is a statement that two algebraic expressions are equal'
2. A iinear equation in one variable is an equation that can be
written in the
standard form
3. When solving an equation, it is possible to introduce a(n)
--
solution,
which is a value that does not satisfy the original equation'
4. Many real-life problems can be solyed using ready-made

equations called
5. Is the equation x 'l 1 : 3 an identity, a conditional equation,
or a contradiction?
6. How can you clear the equation 1* ,
: j of fractions?
Procedures and Problem Solving
Checking
Solution
s of an Equation In Exercises 7-10, Solving an Equation
lnvolving Fractions In Exercises
determine whether each value of x is a solution of the 17-20,
solve the equation using two methods. Then
explain which method is easier.
Values
1(a)r--; ib,1x:4I
1
(c)x:0 (d):r:;

r61198.r*;:i @)r:-2 (b)x:1
1
(c) x: i (d) x: 7
t.+1 + 3:4
fr'*': 810' .l
:
equation.
Equation
,, 1,!:.
" 2x -rr
'r.# -+:4 tt. ;t - ro:6
,r.+*t,:1 ,r.+-2r:f
(a) x: -3 (b) .t: 0
(c) r:21 (d) x: 32
(a)-lr:-16 (b)x:a

(c)r:9 (d) x:16
Solving Equations In Exercises 2l-10, solve the equation
(if possible).
21.3r-5:2x+1 22. 5r-3:6-2x
23.3(y - 5) :3 * 5r' 2-1. 5(:-4) + 4z:5 -62
txr^5r1 1,/zs.:r-;- 3 20. 1- r-r-,
2lz-41 - 3.r I1r :--r- - i - l0: 28. ^ -it, - 2) - l0Lt' -5 '' r +
100 - 4rr 5ir - 629.- - -6
-t+
17*r' 3l-r
30.
-
:100
11'
Classifying Equations In Exercises L1-16, determine
whether the equation is an identity, a conditional

equation, or a contradiction.
ll.2(x - 1): 2r - 2
12. x2 - 8x + 5 : (r - ,l)2 - 11
13. -5(x - 1) : -5(.r- + 1)
14. (x + 3)(x 5) : -t' - 2(x + 7)
14x
15.-1-i- -x-l x- l
5l
16. :+-:21xx
5.r--l l
31.--:l
1110
1a
-
-
-
""'.-i .t-3 12-9

134
J+. ^T-.'-l r r-J x2',r-6
12
35.-+ -:0r r-)
lOx*3 I
a1
-:-
5r*6 2
2
36.3-2-t
-1.tL
12
L-
x-4 r-237. 6-a)(x-2)

Chapter 2 Solving Equations and lnequalities
Vocabulory and Concept Check
In Exercises I and 2, fill in the blank(s).
1. The points (a,0) and (0, b) are called the
-
and
respectively, of the graph of an equation.
2. A
-
of a function is a number a such that f (a) =
In Exercises 3-6, use the figure to answer the questions.
3. What are the x-intercepts of the graph of y : /(x)?
4. What is the y-intercept of the graph of y : S(x)?
5. What are the zero(s) of the function/?

6. What are the solutions of the equation/(r) : S(x)?
Procedures ond Problem Solving
Finding x- and y-lntercepts In Exercises 7-16, find the
x- and y-intercepts of the graph of the equation, if possible.
Figure for Exercises 3-6
Verifying Zeros of Functions In Exercises 2l-26, the
zero(s) of the function are given. Verify the zero(s) both
algebraically and graphicallY.
0.
{ z.y:.t-5
2
-2
8.y:-1,-:
1
7

10.v:4-x2
5
,1
12. y: -*-/, + Z
4
18.),:4(x+3)-2
20. y: l0 + 2(x - 2)
+1
-5
2
4 3x-l13.y:- ll.Y: ,-x+x
15. xy -2y- x* 1:0 16. x)-jr+4Y:0
Appro,xirnating x- and y{nlercepts In Exercises l7-20,
use a graphing utility to graph the equation and
approximate any .r- and y-intercepts. Verify your results
algebraically.

17. y:3(x - 2) - 6
19. y: 20 - (3x - 10)
Function
zt. f(x) : 4(3 - x)
22. fG): 3(x - s) + e
{ zl. f(*) : x3 - 6x2 + 5x
Za. f(r) : x3 - 9-r2 + 18x
r-r2 r- I
,5 /'(r'):--
--
IzJ.J^'
3 5
26.f(x):r-:-Q
x
Zero(s )

x:3
--')
x:0,5,1
-lr : 0, 3,6
x:1
.: -) 5
Finding

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