Document 6501694

Chapter
1 Need-to-Know
List
Review Exercises
Section 1.1
How to sketch and find x- and y intercepts of graphs of equations
How to find equations and sketch graphs of circles
How to use graphs of equations in solving real-life problems
Section 1.2
How to find and use slopes of lines to graph linear equations
How to write linear equations and identify parallel and
perpendicular lines
How to use linear equations to model and solve real-life problems
Section 1.3
How to determine whether relations between two variables are
functions
How to use function notation, evaluate functions, and find the
domains of functions
How to use functions to model and solve real-life problems
Section 1.4
How to use the Vertical Line Test-and find the zeros of functions
How to determine intervals on which functions are increasing or
decreasing
How to identify even and odd functions
Section 1.5
How to identify and graph linear, squaring, cubic, square root,
reciprocal, step, and piecewise-defined functions
How to recognize graphs of common functions
Section 1.6
How to use transformations to sketch graphs of functions
Section 1.7
How to find combinations and compositions of functions
How to use combinations of functions to model and solve real-life
problems
Section 1.8
How to find inverse functions and verify that two functions are
inverse functions
How to use graphs to determine whether functions have inverse
functions
How to use the Horizontal Line Test to determine if functions are
one-to-one
How to find inverse functions algebraically
1-8
13-18
19-20
21-28
29-40
41-42
43-46
47-52
53-54
55-62
63-64
65-68
69-80
81-82
83-90
91-96
97-98
99-100
101-102
103-106
107-112
'Re-vlew
m
InExer~ises 1-4, complete a table of values. Use the
~solution points to sketch the graph ofthe equation.
1. y= 3x - 5
3. Y
=
X2 -
3x
1
+2
2. Y
=
-2:x
4. y
=
2x2 -
X -
9
In Exercises 25-28/ plot the points and find the slope of the
line passing through the pair of points.
'
@ (3,-4), (-7, 1)
26. (-1,8), (6,5)
27. (-4.5,6), (2.1,3)
28. (-3,2), (8,2)
In Exercises 5-8, find the x- and y-intercepts of the, graph of
the equation.
In Exercises 29-32, find an equation.of the line that passes
through the points.
G)y
29. (0,0), (0, 10)
®
= 2x - 9
= ex + 1)2
6, Y =
8.
Ix -
41 - 4
y = x-J9
-
x2
In Exercises 9-12, use symmetry to sketch the graph of the
equation.
9.y
11. y
5-
==
10. y
x2
=.JX+5
= x3
12. y =1 -
+3
3~; 9
14.
1
X2
17.
+ y2 =
+ 2)2 + y2 = 16
16.
x2
X2
+ y2 =
+ (y -
4
8)2
= 81
ind the standard form of the equation of the circle
for which the endpoints of a diameter are (0, 0) and
(4, -6).
18. Firid the standard form of the equation of the circle
for which. the endpoints of a diameter are (- 2, - 3)
and (4, -10).
®!..umb'er
of Stores The number N of Home Depot
, stores from 1993 to 2000 call be approximated by the
model y ~ 953t2 + 162, where t is the time (in.
years), with t = 3 corresponding to 1995. ~
giaph of tlae model and then use the ~lfrp.h to
estimate the year in which the number of stores Will
.
,be 2000. (Source: Home Depot, Inc.)
@Geometry
You have 100 feet of fencing to use for
.. .' three sides of a rectangular fence, with your house
enclosing the fourth side. The area of the enclosure
is given by A = _2x2 + 100x. Graph the ",garniSfr-'
to find the maximum area possible, and how long
each side needs to be to obtain that area.
slope and y-intercept (if
possible) of the equation of the line. Sketch the line.
.@=3x+13
Point
stope
33. (0, -5)
3
Point,
m = 2:
'.0)10, -3)
m =-2
1
+9
Slope
34. (-2,6)
m=O
36. (-8,5)
Undefined
In Exercises 37-40, write an equation of the line throuqh
the point (a) parallel to the given line and (b) perpendicular
to the given line.
Line
Point
(ij)(3, -:-2)
5x - 4y
38. (-8,3)
@C4,
+ 3y
2x
-1)
=
8
=~
x=3
40. (-2,5)
Y
=
-'4
Rate of Change In 'Exercises" 41 and 42, you are given
the dollar value of a product in the 'year 2004 and the rate
'at which the value ofthe item is expected to change during
the next 5 years. Write a linear equation that gives the
dollar value V of the product in terms of the year t. (Let
t = 4 represent 2004.)
2004 Value
Rate
$850increase per year
@$12,500
42. $72.95
$5.15 increase per year
m In Exercises
43. 16x 45. 2x -
22. x =-3
24. Y = -lOx
In Exercises 33-'36, find an equation of the line that passes
through the given point and has the specified slope.Sketch
the line.
43-46, determine whether the equation
represents y as a f~nctioI:l of x.
.ill In Exercises 21-24/ find the
@Y=6
4), (2,0)
Ixl
In Exercises 13-16, find the center and radius of the circle
and sketch its graph.
,15. (x
,~-1,
30. (2,5), (-2, -1)
32. (11,-2), (6,-1)
y4
y -
=
0
3=0
I
j
,/
44. y
46.
=~
IYI = x + 2 ,
;
,i
-- ~'~.,c'-~evie~v'Exercises'
•. ercises 47 and 48, evalu~te the functlon cls'indic;:afed.
_,'plifyyour ahs"";ers.·
. " " .
.:"
.'
:.
(x)
-14 - yl
1
f( -4)
(b)
(d) -f(x+l)
(c) f(t2)
=,'{~;;:",i=i,= ~ ;
.x
, Cd) g(2)
. (a) gC~2j~rk(~i)"(c)g(0)
"Exercises 49-52, determine the domain of the function,
" rify you r resu It with a graph.
I~ &~~~ises 59-62, find
@ j(x)
= 3x2
x
.. hex) = X2 - X - 6
= 1t +
.f60i(x)
~. '8~ +3
,~,
. 11~x
.
X2 -
+ 25
25x
.
.•..
",
In Exercises 63 and 64, determine the inte;val~ over which
the functi~n is increasing, decreasing, or constant. Gtv e. )< - v,
.' Velocity The velocity of a bail thrown vertically
rtpwaid from ground level is v (t) = - 32t + 48, '
where t is the time in seconds and v is the velocity in
feet per second,
.
+~i
16x
-
2
62. j(x),==:.'x3 -
11 '.
th~ze~o$ of the function.·
= 5x + 4x - 1'
60, f(x)
. h(t)
=
-
;f0~) = ):2+:
,: (a) f(2)
58. x
-101·
®f(X)
=
Ixl + Ix +. 11
,
Y
,64. f(x)
= (X2 - 4)2
.
.'
,y
'
..:" (a) Find the velocity when r ~ 1.
(b) .Pind the time when the ball reaches its maximum
height. [Hint: Find the time when vCt) = 0.] ,
,
(c) Findthe velocity when
~;<;'i,,,~4.Mixture
2.
x
Probl~m From afull Sfl-Iiter containe~ of
40% concentration of acid, x liters
removed and
, replaced with 100% acid. '
,
i~
~~<~"':',,'
8,
~:
t =
(a) Writethe
'afiillcuon
amount of acid in thefillai niiXture as
of x.
In Exercises 65-68, determine whether the function is even, "
odd, or rieither.
'.
"
.
"
(b) ,Detepnille the domain and rangeofthe
function.
@ f(x)
(cj Determinex
if the.. final mixture
ls50%acid.
.
'..
.
.
.
..
'"
®,
In E:X:ercises55-58, use the Vertical Une Test to,
termine whether y is a function of x. To print an 'enlarged
,c:.C!pYofthe graph,go'to tli~\Neb~iteWwW.mathgrajJhs:com:.
=
66. j(;:) =
. .:t
+ 4x
X4 -
- 7
,
lOx"
@fex)
= 2x-Jx2 + 3
'f 68. f(x)
=
-V6x2
.m -In Exercises
that ithasthe
the function.
y
x5
69 and ,70, write the linear function f so
indicated function values. Sketch a graph of
"
, .'®f(2) = -6, f(-I) ~ 3"
'70. /(0) = -5, f(4) = ~8
. -'-,;:;:~
i-: -.-:
~.'
",' ".
"
..-,.::~: .:~! • ~.'.
hiExercise~
ii~80, graph . the"... function
.
. ; " •.:.",-, - >-. , '. ; - : .
' ... ":
."
,.',:
=x' - 2
71. j(x) ~ 3 "-:f
72. hex)
73.'j(x)
74. f(x) =
=
-.Jx
JxTI
:)".
. 102
Chapter 1 ~
:75. g(x)
3
=-
77. f(x).=
Functions
ar:p Their Graphs .
.
76. g(x)
1
= --5
78. g(x)
=
x
[x] - 2
x
Exercises
97 and
~8, use •the
table, ,.
:~.:, .•. , .-.~
; .. '
'-',
,"
';'"
which showsthe total values [in billions of dollars} of u.s .:
imports frbm Mexico and Canada for the 'yearS' 1995
.. through 1999. The variables Y1 and Y2 represent the total
values of imports from Mexico and Canada, respectively.
(Source': U.S. Census Buteau) .
.
[i; +.4]
79f(~;b'{S:4;~'5
~~:;
80.
Data Analysis .In
.. ' k.~~~·:..l!:~-~.-r"
+
,.. '
.
.,
jtf~·Jf'-·~'~;
:~~O.
. :':,~,:1sx :
-
a
5,., x >
j
I
j
....
In Exercises 81' and 82, identify the transformed
function shawii' in the graph. "
...
common
.
®,~
y •.•
.. ,
. ~
144.4 .
1995
62.i
·199.6.
74.3
.155.9
1997
85.9
,'-168.2
1998
94.6 .
;.
.
y
~~.
:-: ".'
i
~
.
.'
'C¥).
,J,,;'"
109.7
1999
I
I
!
173.3
198.3
x·
....~
97.' Use a graphing utility to find quadratic models forI
]1 and Y2. Let t = 5 represent 1995.
.
98. Use a graphing utility to graph Yl' Y2' and Yl + Y2
. iuthe same Viewing window. Use the model to .
estimate the to~ -:a1ue of U:S. imports from .,.
.
Canada and~eXJ,co ill 2005:
..
:.,.
.•
~
.\
.
~
.~
gfapn
.:
.
of the' .\
.,....
In Exercises 83- 90, identify the transformation
off and sketch the graph ~f h.
6Yf«) i" ;",
Mx) ~
84.f(x) '~·fi;h(~)
. @J(x)
. $6.
~,'
..
f(x)
XL
-7' ;
.. -/x
.
'~
',i;::;;(f"';~~)':";~;7t~r~"eoffinfo,,",J~i
9
",
.~:I~I,:··:··,.·;~(x)·-= Ix + 31·L~
99. f(~) .; x ~ 7
1,0'0. f(x)
=x
+5 .
'''':
:11
'~';2,
.,
·,f}?,·f(x)
~~3,'
.89. fe;;)
== ax],
9.0:·~
f(if;;;/Hxl'
'c'
h(x) = - (x + 3)2 + 1 "
h(x) '=--/x +.1 +9
hex)
=
In Exercises
~n
101 and 10:2, determine
inverse function.
~
'y
~..
6' '.
-fx
3
.
'.
+ g) (x){ (b)(f
_.
g) (x); .:
.
I;;~e ..r..Sise,S ,93 and 9,4,fincda}f .og,a.nd (~) 9 d,~ing.
domain 9r~~ch function and f'<lch compositefunction;"
~ Z;: ;:.; :c~:~:!
~
y
~
"":.i,'
:.'1·.100.'~.:.'Ih((Xt.)·)_J-4.~::...,:.,3;,X
~
"
";;rt~~
. (f ~~)(x) == h(x). (There is m~~e'{h~rrdn:e'
~;;rj.e'6·~·risw~r,r'o,!·:.;;·
. ~<hCx)=~; + 2
>~~.~.
.:
:
': - -:. ~.
"'
...•....
9"Ph;~gutility t09"ph
'to determine
'fii~ctio!1 is ~l:le-t~-one a~d so h~s an inv~rse function.
"
1
,,;i;.,
"1·
I
flihcti6n:\J;~'the 'Ho~izont~ILineT~st
~~.~:r~t,'
# In Exercises 95 and 96, find two .f~nctjons f and g such that
'. -
';
x
of
"".
:1'
~
:.:
.~;:~ :t:ti ~~:2~;
"" 19'~Jn~ii~;;e;\O~0106' ••
([Dex) ., (6~.; 5)3'
whether the function
hex) = -[x] + 6
, h(;)'i~; 5[~'::,:9]:
iii In Exercises 91 and 92,find (a)(f
\
.
1
. ®t(x)'~~r::&..
.
104_ f(x) ~ (x - 1)'
106. gG:)=,jx
6
+
th. If
if th~
.
I'
.',
.
Ji
I
I
I
I
iI
(
\ ...
'103
Review Exercises
ri Exercises 107-110, (a) find f-1, (b) sketch the graphs of f
'-;Sj-l pn'i:h-e same coordinate system-and (c) veritY that
:\VCx,.)).
==f(f~l(x)). .
.
.
..,..
,.
=:'~
~U'J--Er.ictionaI Force p.4he.:mctionar force F between
the tires and the road required tokeep a car on a
,,:~::;
..:.,.';-~urye.d\8ection ofa highway is directly proportion-
;~{~1'i:~{~i
-.Jih~~&;~';'r;;';~:~;;i;~:~fai;~~;~:~
~:;;:~~'!:~;
~EXer.:ises 111 ~nd112, restrict the domain of the func- ,.~
i~nf to
an interval over-which the function is increasing'
nd determine f-1 over that interval.
112. 'j(x) = /x -
2/
118. Recording Media
The table shows the numbers y
(in millions) of CDs shipped :in the United States
during the years 1990 through 1999. (Source:
Recording Industry Association of America)
13. Data Analysis
The federal minimum wage rates
R (:indollars) :in the United States for selected years
from 1955 through 2000 are shown in the table. A
linear model that approximates this data is
1990 '
1991
1992
R = 0.099t - 0.08
1993
where t represents the year, with t = 5 corresponding to 1955. (Source:
Department of Labor)
u.s.
0.75
1.00
1985
1965
1.25
1990
3.80
1970
1.60
1995
4.25
1975
2.10
2000
5.15
1955
1960
3.10
3.35
1980
(a) Plot the actual data and the model on the same
set of coordinate axes.
(b) How closel;: does the model represent the data?
J1· !rfeQ§]j.rement
You notice a billboard indicating
that it is 2.5 miles or 4' kilometers to the next
restaurant of a national fast-food chain. Use this
information to find a Iinear model that relat~sini1es
to kilometers. Use the model to find the numbers of
kilometersin Z miles and 10 miles.
,
15. Demand
A company
has found that the daily
28~5 '
'3333 "
"407.5 '
495.4
1994
662.1
1995
722.9.
1996
778.9
1997
753.1
1998
847.0
1999
938.9
,
J
. (a) Use the regression feature of agraphing utility to
find the equation of the least squares regression
line that fits the data.
(b) Use the model to estimate the number of CDs
.sbipped during the year 2005.
(c) Interpret the meaning of the slope of the line~
,model inthe context of the problem.
Synth~sis'
J
True or False? In' Exercises 119 and 120, determine
whether the statement is true or false. Justifyyour answer.
Ii!): R~lative to the graph of j(x) ,,= --Ix, the function
h(x) = - --.Ix +. 9 - 13 is shifted nine units to the
i
:F~:f~~~~E:!~;:!=~~~
left and 13 units downward, t1i~n-reflected in the
t~l".~.',,[.i,.~,!,.!
.. '.',,:.;.:,'
".>-,
.:,
demand.
,e,'
,
..
.
~:
~·?~6.Predator-Prey
I:' '
i~:;<
~\<t7 .
The number N of prey t months
after a natiiral predator is introduced into a test area
is inversely proportional to t + L If N = 500 when
t ~
Wfuid N when
t ~
4.
'
,~fflS~d
g are' two u:verse func~ons,
, . domain of g is equal to the range of f
then the
~'Wri~ng
'. Explain the difference
between the
, Vertical Line Test and the Horizontal Line Test
, 122~'Ifyis 'directly proportionaJ. to x for a particular
. ~~ar model, what is the y-intercept of the graph of
'the model?"
I
j
. f
i
j
i
I
·'104
Chapter
1
F>- . Functions
and
.
Their Graphs
,\
'~
Take this test as you would take a test In class. When you are finished, check your:
work against the answers given in the back of the book.
.
i
I
In Exercises 1-3, use intercepts
1. y
=
and symmetry
3 - 5x
=
2. y
i
I
to sketch the graph of the equation.
!
-/x/
4
i,
I
:";.:,'.i·
4. Write the standard form ofthe equation 'of the circle shown at the left.
'In Exercises 5 and 6, find an equation
of the line passing
5. (2, -3), (-4,9)
through
the given points.
6. (3,0.8), (7, -'6)
7. Find an equation of the line that passes through the point (3, 8) and is (a) .
parallel to and (b) perpendicular to the line -4x + 7y = - 5.
.
8. Evaluatej(x)
9. Determine the domain
FIGUflE FOR4
(a) f(7)(b).f(.~5)
~atea:9~Yalu~:
=
'olj(x)'
~'.j100
~
- 9).'
(c) j(x
x2
.,r'
II In Exercises
10-121 (a) find the zeros of the function, (b) use a graphil1g utility to graph
the function,' (c) approximate
the intervals over which the function is increasinq,
decreasing, or constant, and (d) determine whether the function is even, odd, or
Thelnteractive CD-ROM and J~'tefnet
versions of this text offer Chapter '
Pre-Tests andChapter Post-Tests, both -of wh ith have rahdomlygenerated
exercises with ~iagn6stic capabilities,
(
·neither.
. '\
10~f(x)
2x6
=
+ 5x4
-
,
-
X2
13. Sketch the graph of j(x);;::::
.1
.
11" j(x)
4x.J3=X
=
.{3X4.x2 -1-_ 7,1,
'
12. f(x)
= /x
+ 51
x s -:,3
x > _ 3'
,
InExe~cises 14 and 15, identify the common
sketch a graph of the function ..
'.
.,
,'.'
14. hex) =-[x]
In Exercises
in the transformation. Then
function
NO ~rctph .
16 and
17, fj~d (a)
(f g)(x), and (f) (g f)(x).
0
(f
15. hex)
+ ;)(X)I
(b)
"-7"..Jx 1- 5
(f - g)(x),
..
0
='
+8
(fg)(x)/' (d) (f/g)(x)1 (e)
.
(c)
. .,
,
16. j(x)=
3x2
-
7,
g(x):=! -'-x2 - 4x
In Exercises 18-20, determine whether
and if 501 find the inverse function.
18. f(x) ~. x3 +.8
..-. . ~.',
"
, 19. f(x)
+
5
17. j(x)
or not the function
= l;x;2 -.3/
+ 6"
,
g(x)
= ;,
= 2.Jx
1
has an inverse function,
.
.'
".
I
20: .,f(x) ~'3x.Jx
':':' , :
.....
.. :.-\::
',;
,."
In Exerdse~ i1-'23,find a rriathematical model representing
ca~e, determine the constant of proportionality)
the statement.
.'
root of s. (v' = 24 when s
.
=
16.)
(In each
"
,/
i
I
r
;,
r
(
\....
Review Exercises
Section 2.1
How to analyze graphs of quadratic functions
How to write quadratic functions in standard form and sketch
their graphs
How to use quadratic functions to model and solve real-life
problems
Section 2.2
How to use transformations to sketch graphs of polynomial
functions
How to use the Leading Coefficient Test to determine the end
behavior of graphs of polynomial functions
How to use zeros of polynomial functions as sketching aids
Section 2.3
How to use long division to divide polynomials by other
polynomials
How to use synthetic division to divide polynomial by binomials
How to use the Remainder Theorem and the Factor Theorem
Section 2.5
How to find rational zeros of polynomial functions
How to use factoring and the Upper and Lower Bound Rules to
find zeros of polynomial functions
Section 2.6
How to find the domains of rational functions
How to find the horizontal and vertical asymptotes of graphs of
rational functions
How to analyze and sketch graphs of rational functions
How to sketch graphs of rational functions that have slant
asymptotes
How to use rational functions to model and solve real-life
problems
&116'n 2..4
h\(\~3~(\(h~\\\\'u~'\bers.
1-6
7-18
19-22
23-28
29-32
33-42
47-52
53-60
61-64
89-96
99-110
111-114
115-118
119-130
131-134
135-l38
R. e. vi« w:,
~
.
. ..
187
Review Exercises
.,
'Profit, A real ..estate 'offic:ehandles 50
" :a,p~~nt
Units.,When the r~'[)tis $54o'per~ont1i',all
"uJ;Jltsiie
occupied. However, for each$36:intieai~
in ::tent, one unit becomes vacant. Ea(:h ocpipied hblt
requires an average of $18 per month, f()'r~erVice -and
"rypairs .. J.{hat.ieIl!,shou1~ Q~ charged tooPta.iTI. the
~a~!.·" 20. ·M.ax(mijtri
In ExEffdsesl-4r find the quadrati~ f~riai6~
ihat
and whose graph passes th;o~gh the
eindicatedvertex
Iven point.
2.
y
',' '"
, r;;;:{:~a;::;:
"V~y
. ~.
,".'
- .
P~~?~~'-soft
.,
manufa~~~r'has
p~od~c:tion costs' of .,
'
",
•..
:'.
J
.
',"
",;:'"
, C,"",'70,000 '~ , 120~ + 0.055x2
3. ertex: {I, ~4);Point:
4. vertex: (2,3); faint: (-1, is)
"
'
'5. a) /(X)=2x2
"6.
(c)h(x)
(b?g(x)
+
=
,Cd)
kCr)
=
~
o·
approximated
bythem6del
,y = -O.107:X2
"':"'18.5; 20:::;x, ,::;;25,\YhereyistlJ.e~ge
~2x25.68x
±X2~1'
of
'
,
grocn~~6?
(SouTce:T.tS.'Censlls
~cltff 'm
' ' ' "
In ~~rcis~~ 23-28rsketth
. the tfa6sf.()rmation,"
. '
2~";:~i3,::j(~),'L
'"
I>.g(x)
C" ~-h;.
8. f(x) dIU _~;
= x + 8x + 1010.'
h(x) = ,3 + 4x,-- j:z
iflL f(t) == -2(2 +'4t + 1 . 12:j(x) ~:xi 7'- 8x'J: 12
~ 13. hex) = 4X2 + 4x+ 13 l4.j(x) = xi ~6x
27.
i"15. hex) = x~ + 5x 16:j(x) = 4x;
4x + 5
;f".
24. Y T'
9. f(x)
(X~.,
1
'
d ''
+
+1
:3(x2 + 5x ~ 4)
~~ 18. f(x) .~ ~(6X2 '.c-: 24x + 22) . "
~~~,
17. f(x)
='
!~:~':&YT'1>~perimete,
~'
~;r
~.
~',
:'
(~~,4)3 ,
,~,2,~~4
" '. 26. Y==.X4, j(x) ~2(x:-2)4
y;';'
28, y
~
.
x5, j(;)
'=:=-:&~3)s'
i
x5, j(x) ~ x5 + 3
.
:;-;.
~~
",
I
~hd
In Exe.r(j~es29~32,d~t~r~ine;h~rigN-h~~d·
left-'hand
'behavior 9f th€>/graph~ftj,e'pcilyJio'mjal
function:
;"",'
Of a rectangle is 200.
(a) 'praw~ rectangle that gives a visuali:~pr6;6:b.t~~"
tion of the problem. Label the length .and width
in termsof.» and y,respectively ...·)/:..
(b) Write y as a 'fui1ction of xUse
the area as a function of .r. '
of y = x~a~d
r'. j(xh~~x'
y=x4,/(x)
25.
Bureau)
the graphs
·•.~3~2~/hf(th)*~~;#:~~y,:::6pxl.~lxj
E~
+
of the groomand
x is the age of the bride. For
what 'age
the bride is thb average"age'()fthe
In Exercis~~7-18, write theqtiadratj~functionin
,'form and" sket~hjt5
graph.lpentify
theverte;:~nd,
"~'x-intercepts.'
,
22'm~,'~arn~i?a!~gye',"'f'o"Thr"a~~a:ev:reangeaaggeioOffthth',
,6e','~bon9dme,'a,'c(an'a.,
fir,'.bset
(d) k(x) = (x + 2)2
0) g(x) ,=4 -r- xZ,
2
4
;,:(x. -:- 3)2
day
,'
~ Exercise~.s,and
6r graph each .function. Compare the
raph of each functron with the g~aphof y == X2.'
(c) hex) =x.?
(a) j(;Y=,x2.-
whereC is fue t~tal cost (in do1iar~)andi'i~i:he
, number of units produced.iHow m~yunit~sh~uld,
,','be produ~~deacli
to yi~ida minirrlllfucost?'
(2, -3)
.
.
x=
,~x '-'-:7x-:+ lOx
"
I
r~:.
I
I
tile r~s;Utto ~te
(c) Of all possible rectangles with perimeters of 200
meters-find the dimensions, of the one with the
maximum area,
I
I
'}
I
Chapter 2 . J>-
188
_r-..
':~
','.-.
'.
.'
..
.,
..•
In'~~ids'e5 39-42~sketch the g'raph' of the function by (a).·
applying the leading,Coefficient Test, (6) findiiig the zeros
of the polynomial, tcJ 'pJettin~ ~f~liimt ~QIQtl6np1§im~,
,,~tf~awffil;p~~.
gBf(Xl ~
-X' +'x' .~~' . .• ~O.g(x)
41. f(x) = x(x3 + r ,-'
5x-+ 3)
44. hex) = 3x2 .: x4' .
'. .
44.' f(x~ ==
45. f(x) :=
=
4(i'. f(x)
.m
5x
X4 -
-r-r-
+ 3x3
7x4
+
1.
-
8x2
(9
24x2-x8
47. .
.
.
3x - 2
5x3
-r-'
13x2
-
49. ---.-----------
+ 2
+
,
x-I
e.
-
54.
0.1x3
4x3
.
27x2
'2
-
-
'CJ
19x2
5t4
.(b)
8t
-
+ 20
g(.J2)
In Exercises 61-64-, (a) verify the given factorfs) 6fthe func'
tion t, (b) find the remaining factors of~ (c) use your result
to write the complete factorization of f, (d) list-all real zero"
of i, and (e) confirm your results by using a graphing utili. -.
..;'
Factor(s) '~.
= x + :4x2 - 25x - 28
2x3+ l1X2 .: 21X - 90
@r(x) = x4 - ~X3 - 7x2 + 22x + 24
64. j(x) = X4 -l1x3 + 41x2- 61X + 30
.
'2
18x
. ·69..
.'
=
65-68,
(x+ 2)(x-'-:'3
ex -
66.3
+ 3'
in_
:i':;:!~l
- '~~25
68. ~5i
t
I
2) (x - 5),1
write, the c~rTlplex:..number
+
i2
,
''';~
~>
((~5i)~:)-~+(5z.~.
-12.)
-+-Z
2
2
t
-
2
. r}.'j.
",·21
2
'~
-~i)Jl!
7'1: 5i(13 - 8i)72.
(10 -'- 8i)(2 ~ 3i) ·74.
.. @
.
,
+ 38x + 24
+ 29x
(x - 4)
(x +6'
3
'70. -.--.
.; In Exer~is~s 75 and 76, write the
. 6+
~::~75:
4-
x- 4
3.x3.__+.2.0X2
56. -''-c'-
<
In Exercises 69-74, perform the operation a~d ~rite th~t
result in standard form.
x+ 0.3x2 - 0.5
:;;;-5
Q2x3
+
(a) g(-4)
67•
In Exercises 53-56, use synthetic division' to divide. .
6x4
....,.f~
(d) x=
(b) f( -1)
-
'(jj):a::;;
-2--
.
···
. 60. 'g(t) = 2t5
m In Exercises
3x4
+ 4X2 - 6x + 3'
51.
2 .
. .
'.
x +2
6x4 + lOx3 + i3x2 -r-: 5x + 2
52. ~----~--~~~----~
=.!
. ;'2x2~
i
53..
2"1
X==;3
+2Q~ +44
= x4 + 10x3 - 24x2
62. f(x)
3x3
@
(c)
·/f~
61. f(x)
2
50.
x2-3x+l
x4 -
+?6 .
-4
Function
\!
48. 4x + 7
3x - 2
X
20x
.
6.12
In Exercises 47-52, use long division to divide.
·
B
-.:
x==
. to graph the function.
3.6.5x
-
(b)
(a) f( -3)
+3
X2
0.25x3
8x2
-
' .. (a) x=4
@f(X)
use the Intermediate Value Theorem
and the table feature of a graphing utility to find intervals
one unit in length in which the polynomial function is
guar~'nteed to have a zero, Adjust the table to approximate
, the zdros of the function. Use-the zero or root feature of a
graph'ing utility to verify your results.
.s:
== ,3x3
58. f(x)
.:;"~
In Exercises 59 and 60, use synthetic division to find the.·;:C
specified vai'Ueof th'ei fu~ction.
. ..~"
= ~ + 4r
II In Exercises '43-46,
43. f(1) = 3X3
-'-~-",:I
Polynomial and RationaI Functio!1s
- _12
.
,
in sta~dard forl11:~~
qUO~~t
Z
i
~1. + ~i)(5
1(6 + z)(3 - 21)'Y~
-.
.
.....\~;~
'.
{,;,;,\3
~5
+ 2z...
+i ,
"~I
•
.
~~
x+3
In Exercises 57 and 58, use synthetic.division to determine
'whether the given values of x are zeros of the function.
@ Ax) ., 20x +
4
.
. (a) x = -1
9.x3 -1~x2 .; ,3x
3
(b) x = 4
(c) x = 0
'
'.,'.'
'
(d);t = 1
-:In h~~ci·se.~'i7.ani7'~;,~e·rf~rn:~h~~;p;ratr()n9ri.dP~i~eth~~·
. result In standard form.
.:
..'
.. .:
, ..
4 . .
,
77. 2'-'- 3i
2
"".,
+ I' + i
.'.' ,
"'l
·1 ..... , ·'5'···~'.
..,/ 'l'·
'78. 2 + i -: i
+ 4i;I~ -.
~
'1~"Exerci~e5 1 07 and 1 DB, use Descartes's R~le of Signs to
, d~t~I;m}netV\: possible numbers of positive and negative
ercises 79-81, find all so/utiohs of the equation.
+ 1=
. 3xz
, " 80. 2 +'-8x2
0
+ 10 = 0
:;.1-:Lx
82. 6x2
=
0-
.,;e~r():,pf!h~f~nC~iO~..'
+ 3x + 27" = 0
101.:g:(±) '~ 5x
3
,.'.,.-
~fex:)
=
(x.- 4)(i-
~j(x) == x
3
+
+
.' (x) = X2 - 9x
+ 6x
+ 4)(x
.
9)2 .
,'.
.~
•.
+
'.",
3x2
,."
+9'
-6x
";,
'.
+ 4x3
~ •
," 'J.
.:.... 2x2
•
_
®f(X), = 4~ - 3.i2 + 4x - 3
.v ' :."',',
, i(x)
"
== (x -": 8)(x -,5)z.(x " ;3 + i)(~ -
-~ 6) (x - 2i)(x
'
"
" (a): Upper: x 0;= X
+ 2i) .
=
'!, \.~.;
+5
In Exercises'109 and 110, use synthetic division to verifythe~ ,.'
upper and lower bounds of the ;'e~1zeros off.
' . . ..'
8
;:"fex)
(x
,:".:
:I.OK hex) ~ :""2x5
In Exercises 83-88, find all the zeros of the function. '.,
, f(x) = 3x(x - 2)2"
139
ReviewExercises
,
1.
•
x=;"~4
(b) Lower:
"
..•
'r-
".'
'",
-:
.....•
".'
.
Il!),
3 -, i) ,
.
.
..
==3x4 + 4x3
-
5x2
-
. f(x)
.
(x)
", f(x)
5~f(x)
,c.
f(x)
x3 +'9X2
+ 24x+
=
-o-';14x
8
+8
'(b) Lower: x
=
·....:4
m
8'
Gf(X)
~
'L:\r
'" ~(x)
= x:3 - 2x2 - 2lx -:- 18
== 3x3 - 20x2 + 7x +. 30
=7 x3 'lOx2 + 17x ':'::'~8
==
5X2
In Exercises 111-114, find the domain of the,~tlonal
function.
'"erCises 91~96,find all the real zeros of the.function.
'. (x)
2,x3 -
(a) Upper: x
erci5~589 ~nd'90, use the Rational Zero Test to list all
ibrera~i~i1alzeros ofr.
',' ',',.'
'"
..
.;,
.
;, (x) = -4x3 + 8x2 -r- 3x + 15
,:'f(x)
f(xY:=
-rr-
_5_X -·
I
I
112. fex) ='1 ~~x
1
'X+
~
'x2+.x~2
=~2-:-:~Ox-t 24,114. fex) = X2
+4
j
)
20
':
In Exercises '115;-118, identify any horizontal or vertical
asymptotes.
:.
'Q,(x)
+ x3 - 1l~2 + X - 12
= 25x4 + 25~3 - 164x2 4x + 24
= X4
",'~
"
,
=_4_
x+3
X2
»r-
"@g(x)
xercises 97 and 98, find a polynomial With real coeffi,Ilt;thathahhegh)erizeros~,
:" '
'.,,'
"
".;
,.,.
98. 2, -3, 1 .: 2i, '
=
X2X~
'/
,:I
== 2x2 + 5x - 3
116. f(x)
+2
'
I
1
118. g(x) = (x _ ?)2
4
I
In Exercises119-130, identify iritercepts.es '±ti¥l'l1metry,
identify any verticalo~ horizontal asymptotes,~
"~1?f'oElQf£'Tirtt$.,
.
~
Q
ercises 99-102, use the given zero to find all the zeros
he function,
'
,
'
',"
,','
I
I
,4
120. f(x) '= x
Function
Zero
I
'/
x- 3
122. hex)
=
x-.:...,-z'
I
,
I,
124.
f (x) = X2
126. ',hex) =
2x
-1-
4
,.
4
ex ',_'", )2'1
j
"':,
I'
.I
/
I'
"1
2x2
,,~~.
j(x) =.x3 +4Xl -'- 5;r
4·-g(x)=
,'~:'i(x)=
~
X4
-.7r+:36
+4},~" 3.il + 40~ + 208
'G·f(r) = 'x4 + 8.:2 + 8,il - .72x - 153
,
,'129. y
, :'
";''';''x:''
=--,-'
'x~
-,1
~,~ X2
,-,.4./
:.:.'.2 .,",./
13.o~ g(x).'= (x ~ 3)2
I
, >/1
I
'. s
190
Chapter 2
);>-.
Polynomial and Rational Functions
. In Ex~rd'ies 131-134, state the domain of the function and
~s¥5IedI!I WI~
. ", .Identify any vertical and slant asymptotes,
y =
18,47x - 2.96
0.23x + 1 ".
x>O
j~~-:._,
,.~
...
:'.,
.:,_,·i~:'~;]·:;:~;:.Il:f!
co.
.
•
.:'
.."
.
135. Average Cost
C
=
•
A
C
business has a cost
of
O.5x + 500 for producing x units. The aVl?rage',.,
~'"
~r
C=
-;
":'5: + 500
= --x--
x >
Jractio'n 'decomposition for the rational expression, Do. no
f~r the constants.
.
,
';"
140'~iJi~
139.X' : 20,
141~x;x-".~5;2
O.
'Determine the average cost per unit as x increases
without bound. (Find the horizontal asymptote.)
136. Seiiure of Illegal Drugs
.
"sol~e
28
142·:;(xz.+ 2)2'
':'!
The cost C (in millions .
of dollars) for, thefederal government to seize p%
of an illegal drug
it enters the country is
In Exercises 143-150, write the partial fraction decompos]
.tion for the rational expression.
-x
144. --'--'--~
as
C
=
528p
100 - p'
X2
0:::; p < 100.
(a) Find tl!e cost of seizing 25% of the :drug.
147.
+ 2x
'(b) Show that the total area A on the page is
A= 2x(2x +7).
.
x- 4
.'
II(d)Use.a
graphing utili1:y to graph the area func.tion9-lld approximate the page size for which
the least amount of paper will be used.
The amount y of CO2 uptake ill
'IDilligrams per square decimeter per hour at optimal
t.c:;mp~ratriresandwiththe
146.
9
j:2_
.'
. 4x - 2·
9
)2
+ 4x
4x2
149·(x2 + 1)2
150. (x - 1)(x2
+ 1)
:::
Synthesis
True
or Fali~? In, Exercises 1.51 and 152, determin
whether the statement is true or false. Justify your answe
151. A fourth-degree polynomial can have -5, - 8i, 4,
and 5 as its zeros.
152. The domain of a rational function can never be
.. sdof
~real
numbers.
153. Write quadratic equations that have (a) two distim
. real solutions, (b) two complexsolutions,
and (b
(c) Determine the domain of the function based on
the physical constraints of the problem .
·.ml138. Photosynthesis
+ 3x + 2
148.' (
3 x-I
2
3x3
(a) Draw a diagram that gives a visual representation of the problem.
.
- 15
x2 + 2x
3
(c) Find the cost of seizing 75% of the drug.
A page that is x inches wide and
y inches high contains 30 square inches of print.
The top and bottom margins are 2 inches deep, and
the margins on each side are 2 inches wide.
',;
X2
(b) Find the cost of seizing 50% of the drug,
137. Minimum Area
.
. 145. ---:?'~--~
x-x+x-1
(d) According to this model, would it be possible
c
to ,~eize 100% of the drug?
.
j;2
natural supply o.f CO2 is.
' ,.......
. .
.':~ppihxi.Iiated by the' model"
no real solution.
= a(x - h)2 + k, state
.
values of a, h, and k that yield a reflection in ¢
.. x~~ ;'ith either a shrink or a stretch of the grip
of the functionj'(x) = X2. "
154.' Gi';e~'the';~ctionf(x)
(; '0.
)5?
'
.
What is the degree ofa function that has exactl
'·two real zeros and two complex zeros? .
. .-1.56. Because z-2.= ~
, "'riWn:~~~'a~eal
1, is the square of any compI
number? Explain,
."
.
Pra.ciic
.' •. ' 7..: ", ~'.:
; ~,
,!"
e
Chapter.Test1ST
.• -:~'!;'~:',\:,(~:-=~-: !.:->~,\:
•.
~\
::·~~-·':··--;;~~···~·~l':+·~<
... :.'
"';',
v •
,.,'
<.,:,'
.
"',
_ .•
.:~r~"'-=·;,.,.
:
"
_, .:.
.
<:(::';::\.
:
·
:- Take thls 'testa's you would take.a test in class. When you are finishedcheck your
· ..:' .' iiJb~~ag'al~5t\heanswer5 given in the back ~f the book.
:.'.-
r
1.;es~~~~hOW
, (a)g(x)
=;
.(b}. $(x) =
fuegraph~f
2 -
i diffeT~'fro~'~egraPh
off(x)
= .:
~2
(x -" ~y
2. Fmd an equation of the parabola shown ill the figure at the left.
~?oX2 +
3. The path of a ball is givenbyy :;=
3x.+ 5, where y is the height (in
. feetjof the ball and x is the horizontal.distance (ill feet) from where the ball
.was thrown. Flnd (a) the maximum height of the ball and (b) the distance the
ball travels.
.,';,
4. Determine the right-hand and left-hand behavior of the graph of the function
het) = ":"'~t5+ 2t2• Then sketch its graph.
5. Divide by long division: 3x3
. e Interactive CD-ROM~nd Internet
+ 4x -
X
Perform the operation and write the result in standard fo~.
(a) 10i-(3+-J~25)..
(b)
·
.: ....
..:
-;'
':.:~',: .
9:g(t)
5'
(
;
? .and
~ 2t4
-
10, find all the' real zeros of the function ..
3t3
+ 'i6t -
.y(Fin'd~ zeros ofJ(x)
;
.
.
.
. ".
".
the 9l!otient in. standardfo~:~i+
lnfx~rcise5
':
.'
;(2+.:.,)3i),(2 - Ai)
.'
X·Writ.e
..
1 -7-:xl-+ l.
6. Use synthetic division to show that x = A is ·a zero of the function
Jex) ==: 4x3 - X2 - 12x + 3. Use the result to factor the polynomial function
completely and list all the real zeros of the function .
rsions of this text offer Chapter
re-Tests and Chapter Post-Tests, both
fwhich have randomly generated
.,ercises with diagriostic capabilities.
= X4
. 10~ hex) ~.·3:x5
24
-:-
x3
+ 2X2
'-
+
"',
~4
':
.
.2
$x -
4x - 8 given,thatJ(2i)
:;=
O.
j
',:
'.
...
.
'. In.Exercisas 12 and 13,find a polynomial function with integer~oefficients
i the giVen zeros.
·.?t~·6~:':~'
~i:
v ".
3 - i
',~,1
,+,'~i;l
"'".,
1
I
~.J3i,2,2
',: ," in'Exerd~~s' 14-16, sketch the graph bf the ratio~aJ function
'> •. c·, .' 'idehti:r:Y"i3J1,intercepts
and asymptotes .... : . . ..~...'.
.
.
that has
'py
hand.Be
. .,.,
s~tkto
'1
I
I
....
I.
." :.' x2+2
;'16 .. g(x) '7 .../ ..... .
.
.;
.
.-:.
x;""
:. l~'-~'
..J;.
1
I
.>
. '. f ~
r-: ':':'- ,::. ',I ..• ,
I
"
,-"
2x + 4
x2(2':"" x)
3);2 -
20.
'x2
-4
x3
+2x'
f
i
Chapter 4 Need-to-Know List
Review Exercises
Section 4.1
How to describe angles
How to use radian and degree measure
How to use angles to model and solve real-life problems
Section 4.3
How to evaluate trigonometric functions of acute angles
How to use the fundamental trigonometric identities
How to use a calculator to evaluate trigonometric functions
How to use trigonometric functions to model and solve real-life
problems
1-4
5-20
21.,22
39-42
43-46
47-52
53-54
n - . ··\X}"', ..··--_··,·
tx- e V i~'.·
~
III
one-half
Exercises 1-4, estimate
radian.
·21. Phonograph. Compactdiscs have an but repjaced·(·i
phonograph records-Phonograph
records arevinylv
discs that rotate on a turntable. A'tYPical record '
album is 12 inches in diameter and plays at· 331
revolutions per minute.
3
the angle to the nearest
. .
l°L
2.. ~
3'A~
4'0-
.,:. ..
(a) What is the angular speed of a record album?
(b) V0Cit}s the linear speed of the outer edge Of a
.reccird album?
.
22. Bicycle At what speed is a bicyclist traveling when "
his 27 "inch-diameter tires are rotating at an angular
speed of 57Tradians per second?
'j
I
I
4
!
.
~
In Exercises 13-::J 6, convert
degrees: Ro'tind}our~nswer
0;:',' ..
·.c
..~.
-
to
.
~
.:
:.
;",i
the measure from radians to
two decimal plac~s.· . •....
14'
• r '
111,
6
,"
6
... ".'~.-
.~I. '. ';,'
.
, 42 .
r
. 15. ~3.516.
.
.
5,,7
.
111'.Exercises
17-:;W,
·radians. Round your answer to four decimal places.
·"Y.;.480
\..[!.)
18. - f27S
~ '19. -33°45'
20. 196°'77'
0·'
9
convert the measure from degrees to
.
e
5
0 ~
o
00
~'~.RailTDadGrade
43-46, use the given Junctjpn '1~J.ueand
m~~dc identities {including fhe'~bf4ncticir{;la¥nti-
"''lcises
find the indica~ed. trigonometric
.
TIJl1dions:-'-
;
A tr@l""trav~~3.5 kilometers on a;
.straight.
track-with
a ~Je-of-~r10"
C·'see.: .... .u.gore}
.c;. '.-.' ;~:'--'-'
'.. . '.
.~'''c._~~~
.$+"""
.....
..
.:Wb.at:iSthe vertical rise of the ,train in that distiji.2e?
-,0:0 •.
-.
1
{1==3
eSG
e
(b)
cas
e
see
e
(d) tan
e
e=4
j
'e
')
cot
e
(bj see
e
CDS
8
(d) csc
e
r,iy ~re
e=4
SID e
(b) cas
e
) see
. (d) tan
A ~y wire Tuns from the ground to the
top of a 25-foot telephone pole. The angle .formed.
e
between the wire and the ground is 52°. How far:
e
from the base of the pole is the wire attached to the
grolJJJ.d?
'sc e = 5
a) SID e
c) tan e
. (b) cot
e
r
(d) see (90° ,- e)
.
"
{,. ;.
,~
'. rcises' 47-52, use a calculator to evaluate the trigona~functian.·Round your answerto two decimal pl~ces.'·
k>,
;
348
Chapter 4
~ ~:Trigonom~try'
Take this. test as you 'would take a test in class, When you are finished, check
work againstthe
answers gIven in the back of the book.
00nSideran.ang1eth~t
y
measures
51T~:radians.
, ,(a)Sfetc1:;t the angle in standard pOSID.On
.
.(b)' Determine
(c) Convert me angle to degree measure.
x
.·2.
FIGURE FOR 3
.two coterminal angles (one positive and one negative).
it
~i
A truck is rnoving at a Tate 90 k;il~:i:rieters,per hour, and the diameter of
.wh~e1s is 1 ~~16i~'FiJ1d
the angclar speed of the wheels in radians per mlnU(
3. Find the e;il¥t'~~~es
..in the :5guTe':0jYkF(:
CV;~~en
o
.
o.~~..
that
"0
of the six tri~ono:r:o.etricfunctions of the angle 8 sho~
..
~':~:F~,:find
the other five trigonogletric functions of 8,
.:o;}~~~~t~~o~
.00.
•
:.0
~o'.
'):
};,,~
.;
.j
,!,;
,"';
Al06
:.nswers to Odd-Numbered
Exerer,e, and Test,
71. <a) and (IJ)
allclTests.
Answers to'9dd-Num~~led·Ele:rclse.:s
l:t:'· ..
,g 17S
~ J'p
..l ''''
~ 0; y-intercept: CO, 6)
3; y-Intercept;
(0,13)
23. m ~
,
53. (aJ 16 f~et per seccnd
- (c)
-16 feet per second ',
"55. Function
i,
59~ 3
1~i):
1I I I I I I 1.
.1) " 50 1(1 100
·rtlc:.('~lQ)·
Ce) Y'~ LOat.+ 17.7.1
(0) part (b):
57. Not
'J
(d) Tho models are similar.
232fcet;part
(e):
240.02foot
-2
5.
(1) An&!.l'S~"'Mll '1''''1-
(~I0) .
x-intercept:
.,
,
y-intercept: (0, -,,9)
(4 ..5,6) I
y-axis symmetry
.•..
"x
qqestlonable
.
-
when based on su~h limited
=
-1
-:-f--t--t-+-~ ..
-;-{ 7"1_~ ..1....
,6
,
2y -:
=D
10 = 0
35. "
+. 2y
-
4.~
~
}
H-i--H+JI
-1
-:1-"
,,:..
... ...
'..
-~
,
:
I
~
..
15.'
73.
~ 8
°
3
a
.1
.,
~t--t--t--+-
-3 _1_,
0); Radius; 3.
2. 1
"' ,.J
.•...
!.
..-f
,'.
6
..
•.
... t
+=
-f-H-H
-~ ..-"...,
'
-l·
"
13. Center..{O,
.~
~1,.-
.....
si. Ax -t- 3y
0
]x -
willlnerea86 If Ji is posltlve and y will decrease if
k i<negatlve.· ~ ..
data.
-6
-t-+--f-"H)-:J.
1 1 , •.
.
--+--t--t--
-!
m=
Bachyear, the annual receipts for motion picture movie
theaters her ••••es by $412.9 million ..
79• x s: 4,"':?
(3,-4)
-.
75. False. y
,,:
..
-4 ~3-1 -L1
..
.~..'.:: Iii;
.
'.:
-+-+---t--+--
4:
j
+ 3642
77. The tlCClJuwy!.~
_
,(1.1,3)
-.
Cd)2000: ~1771.0million; 2002: $8596.8 million
(0).
l
j
.
CO, 1)
.j-Intercept:
9.
11.
.
'."
t .
,
I
67. Ode}
65. Neither even I!or qdd
69. f(x} = -3x'
7. x-intercept; (,-1, C)·
41291
-ll
Constant on [-1, OJ.
,
&
1 ',.
a functicn
(0. 00)'
on
Deei~~ing.,,~(:"00,
73. ~l)and (e)
(b}.R ":
-+
Gl:
63. Increasing
t.+121
y~
A10?
.(\» 1.5 seconds
-,
81. x> 5
-j
-s
~
I
:&
83. (a>
thv\
J."
-I.
J'
(b)
[I
'"
-t
'I
II
(
I
$.6,
(e) 21
1
....
I I
..
. (a) 5x - 4y.- 23 ='0
Review Exercises .. (page 100)
i
1:~2""
.".:"- . -!
.
-ll
-8
:',
0
.1.
-5 .-2
2
1
+ 3)'=
17, {x - 2)1 + (y
13
{{43. No
19'1:~tLH /.
~ uoo·
~
i
1000
~
soo
:'
~
i'1!47.
.
,
Il)j
H 1991)
(b)
17
(c)
t' + 1
19.
,..
5y - 2 ~ O·
.e-o..
,"
4-~~~~'
-l-1 -I
-<J
J " ..~
.t
-'.
(d).-.•'·;:-2x - ~
.51. All real numbers
~:
~.'
~n'
?:;~
',
,
a
-I-+-H-l
-Jj-'~-3
0-0
e-o .-J
-0
-6
-I-l-t-I-t-+-JI
1 6 , 12 11
_I:l
~
-13
x oF 3. -2
"'"
L
r, •
iii,.'.., ~>-'--t-If---<.....,..I.;-
fJ~~~
,
0-<>
t~
I'
'.
.
!,?
.
.•
3'6
Yu.r(3
2004
"
+
45. Yes
(a) 5
1:~~9.:;:5$·x~.5
,
':
(b) 4x
77.
-0
~;N9, (a) x = 4 (b) Y =: - l'
i~i1.V = 8S0t + 9.100, 4 '.:5: t S; 9
./
;
(10,-3)
,~l-'l
jt
<:,
~
..__
.J
-
. "'--"
A10B
Answers: 10 Odd-Numbered
01 nln. units downward
83. VCltical.hift
'~'
-'\
95. lex) = xl. g(x) = 6x - 5 (An~weris not unique.
Answers to Odd·Nutr/oer.ed "Xercli.5.nctTe,ts
97. Y,'= 0.207" + 8.65''+ 14.2'
y,'= 1.414,'·- 7,28' + 146.9
-H--f-:-~
Exercises and Tests
'
_2
:to
-I
x
I'
r
99.
•
l(.)
= x.t·7
a),,~
103.
~=".,
'. l·~:1'
The functlon has. an
.u,...
shlfl of three units 'to the left and vertical. shift
ofiiye unlts.gov,nw.rd
-a~"
f·
105.
.8....
Ej,,..
-s
.,.£
.....
-.).".;
..
il.;:.i:
.
•
•
'
.1
.
.
:'
:1"
.he .•ctual data.
.'
','
.
-..,
-
.. ,
(.
'3
','
(b::"-'~"~":"
'4
-11
(c)
r'(ji,x» =.i(tx - 3) + 6 = s - 6 + 6 =
~(17+ 6) -3 - l';' 3- 3 .;,
109. (a) rl(x)''''.x'
.
(b).
D
"".,
- 1, x ~
Cv\.\
a
'y.
,
..,
.Y
,.
."
(c) 2x'.:: ,:' +6. - 3
'~3, (a) x
+..~x' + 3
-l·
(I:i) x •.,.
(d) 2. _ I' x
(c) /-I([(x»
1
*;;
8
Domain off, s:,f. 8. and g 'J: ell real'numbera
..
= r(..fi+1): x:> -1
- Jx'
. . .',,\ .
. ,1
1
(c) racr~"jllg
~.
':-4 ,:"3 -:1'7!.1+~·I','3,"
.:
•
r:
(4,0)
13.
~"..:1
,,'
"
-12
a
\~~,. y-axis·symmetry
•
'-1
Oil (
-s,
(0)
t~
....
r....
(~)'·~*i~~?;~~:~~·-·5~.':,'>;::j,~~
;
"
~, .
.:,,·(X+·l) -'1
= x',
f(f-l(X»'=f(x'~
1), x:> 0
.
.'.'\
:.".
.
"
~(O,~)
',':
'I',,"
..... .:
;
(b):':::.~
-s
I.
+ 2<.+ 2 .. {b) ~'-'2>'
(-00,:1.)
(ai~:-5:·.··..·.,
,':
.I ••
"
•
0)\
. "D~c'~••Jng on (2, 3) .
'(d):treiUteJ .v.nll~r~ad.
H.
H,O)
.
(e). jnclo""ing
2. taxi, ,ymmetr5-
"'~'((')
x'
.
...11
"':"
. No sYJl'\llletry
..
91 (0)
"
,
. (page 104)
apter Test
• _"',
,
'
. Jtr'(x»:.
0). (Q,3L,;"';
-O.31i::(o.o:ilJ) .
11, (.). 0, 3
Line Test is usee! t~'determine if the graph of
y if'a·function of x, The'Horlzontal Line Test.is .used to'
" determineifa function has an-inverse functiop, ..
...
;'-:,'1:"':'
ar,.c:-O,31,
'. ,.Xiec;U'i"~ on (..'..cc,
.~'.
.
\ !.
;1
-~1
:(c):It1~'ing
. The Vertical
I
I' ~
~ .6".
11$~ "
0, U.43~"'·
-II
.
x' -
0..
.(d) BV<)l
J.
-3_3
".
(b) .
=a
'('.')"-JX'
'n
·'-E9;E1
n.$~r:" '.
)'1.
.,
I
,,::I,
1
~9
4y - 53' = 0
-1O",;;;:s; 10' .
10. (0)
Palse, The. graph is reflected in.the x-axls, shifted-nine.
~·nii.'rto the..leff,.nd·then ;hifted'13 units downward.
17 + 6
JOJ,,-
,
,",0.50:;
117. Aiactorof4'
!
._4
107. (a)/-I(.).='
69. Relleption in the .-axis·and vertlcal shift of six units upward
O-Q
::.":.;.,
~,.."
,
-4. --1..'
12
.
".
4,
I
'.
·:·667unH, ..
(b)'
-i
L7x +
6.
J
87. R~flection In·the x-axi" horizontal sbift of One unit to the
.1eft•.and vertlcol.llift of nino unit, upward
i..
Ie·· "
,0"30
..
:.(b) The model is a "gooHli':'for
"
.:
10
,
Yen (S +t,
-, .
j).
.
I, •.
.
\:,1
):'L
. , (0.
.
·:~6·.3
85. lIodrontal
••
8
jI']'5
):,109
3)' '= 1.5'
+ 4<1-. = O,Cb)'1",+
7. (a) 4>:- 7y
.•. ~,..
.S.>!·
.101. The function has an inverse.
~ -u·
4'
.
fU-l1;t.»),=i ~ 7 •. 7 =x
i-I(f(x»)
=x - 7 +7 =x
••
ji;, +
', :>,4; [I(X) =
+ (y.-:5,17 + '] -:-l ='0.
4. (x - 1]'
'"
:'\
.,:
\'
~:,'
•..~I-+-,l:·
......
-1 +1
. ~:.,.
~.x
":.'
~.~3
..-4
v •
r- :
,.
.
'~.
. •... ,: ..
II;'
..~'.;.:.
Al10
'\,._""r,
to Odd-Numbered
Exercises and Tests
11.124
14. Reflectlcn In the x-ub ofy = [xJ
0.0
~
,
3. (a) The function wlll be even.
00()
e-o
3
s-o
~
0-<>
-t
-,~
5.
+ ... +
'j{x) = ~I1X1.~+~_1x1'1-2
QlXl
x-12
x(x - 4)
=f(x)
...,
(b) 25~miles per hour
+ 3400
-,
.
'ood~J.-'
11'3500
3001l
9 ,:lSOO .
,
4.x2
+ 4.
-3,,· - 12-' + 2:2.' + :iSx 3x"-T'
.
(d) _,,1.~4.:c + ", x'" -5; 1
(f)
+ 24,1:' + 18":>--
1 + 2:x'!Z
2-./X
7'
+ 68
(e)~,
x
18. rl(x) =
> 0
(t)
.v:x=l'
2:x'/"
:l.-./X
7' x
22. A = ~XY13~
·6
>0
'(6)
X"
(d)
Problem S()lving (page 106)
1. (n). WI = 2000 + oms
(b) W. b
x=
I
(b)
.
_
.... '.'
'1,
,
f(xl=-:--3~:::':4)' +
187)
t.
(~,:;,::..: .. ;.. ,"<.'. .
='1
.'
i.
~2.-!.1.
-('-l
-a-
.
7.- 4x
(b),
-,
:2 \~ ••
.:.
"1;
-4
~2000 1
Tx
'venlcalsbeich .
11-
f(f(x»
.
~u
'.
,
x-I'
= -,-
Domain: all real numbers x " 0, 1
. (d)
=x
. The graph. .is not a line because: there
;= Oandx= 1.
(c)
OO~~'"
2300'+'O.05S
.
J'
"-
~,
I
I
,\1/, ,
I
,
1(.
Maximum: 400'P
Minimum: 266.7'F
8:f1
59. P~lse. The partial fraction decempositlon is
loo,OtD
Both jobs pay the same monthly salary if sale. equal
$15,000.
"
tVl r:t/
.
i !¢ibJ ~R~~i~~!.~K~.r~~;c7.~.'(page
= I'-.2000'1
-
..
Ymin
1
. (c) f(f(j(x»)
,
,',
'~"
(e) 11le dist~ce x = 1 yields a time of 1.68ho
Range: all real numbers
(l5,000,3,OJO)
DR
(bjYmax.
11. (0) Domain: all real number •• '" 1
.
t.',
0' f\'
'P1e vertical asymptotes are the same.
2000
: . 2000
i
57, (a) 7'.- 4x - 11 _ 7x' 0 < x :;; 1
-\
21. v = 6-!S
>,.t< :~.~:.,:"", ..
71"'~~" :~ l~~
r.. ',.
'I:'
·'r.i~----~
,~
,
.
,
4'.Jx1- 6, +10
0
> 0
'
140:1
1
~X"
. "... ~ .
x +'3
, .
.
'..
,,
~
b =~.
a
I,:;",
'l
s
(b)0';x;;3
x
19. No inverse
20. rl(x) = Gx)1/1, x';, 0
(c)
1 rr-r+x
y=-y=J: -.3'
:.
.,
Hours
1 - 2x'/l
x >. O. (d)
.
9
X2 -
·'1
neno
:\"
.3"5
2(4;' - a)
. .
'0
. :
..
'~'.:
~'O-I~'~~~~":-,r
I~ .
;.JO,~IJ
•
3060
(b) --x-'
1
..IX
.
= the. sa~~.
x.+3
.
9, (a) T = '2,,4,+.xl+
0
x,>
'000'
~ 1500
•13.1000
A 3'"
35
-9.' + 3Ox' :..- 10
17. (a) -. -. -,,-..
(c)
120x
3'
- 12
(0)
(e) 3x'
y~'
'jj
16. (a) 2.1:' - 4>=,-- 2. : (b)
69,
~,"
55,~+~
x-3
(d)
-1 ..
-I
The vertical asymptotes
y.:;; 3400
Range: 0 S
•..
,1 ,~
67.
J
..•....
7. (a) 81~hours
:':180
(c).y = -7-'>:
Domain: 0 S x··S !!p
-a
65.
2
+ ao
10
-oj.
3
y=;-.y=-~
",,_,(-x)"'-'
+. , ,+ ",(-xl' + ao
-,
--+--+--l-~'
_l_)
G3.:.!.(1
+_1_)
a-;x
a Y
«<s),
t
. 2a a+.r
I(",:x) = .,,(-x)'· +
....,
~
00()
15. Reflection in the x-uis, horizontal shlft. and-vertical shift
ofy= -./r
,-6
61. 1.c(_1 _
y=--
(c) The function will be neither eveu nor odd.
-~ -l_lt~4
Exerclses and Tests
2-
53. -.,--x ,x - 4
The function will be odd.if 'the two functions are .
'''equal:
.
(b)
•
,OK>
-6
Answers to Odd-Numbered
(d) No. Job 1 would pay $3400andjob 2 would pay.$3.
_A_+~+
__ C_
x"
(x - 10)"
10
:x·-·lO
·Ve[tiCal·tf~S!BU~I1:
.
".~"
:/-
.','.
.-\'
.....
:t'
~:
·;L-
'fl
9. j(x} = (x
+ 4)2 -
6
Exercises and Tests
.
vertex: (- 4, - 6)
l~. h(x) = 4(x
.,
,'
'-
(±../4I
- 5
=:-.2--;
,..
,:tilt'" '
'.'t" :j-:t:l:'~}'
-3
()'..
+ f .-
<,:
~f~i~
.
~}~.
(~t)\
J... .'
-H\J1-----1-+i
-1·-,
.
4'
~W'·
t~"\~'
,1
...e::ertex:
I~~:
(.../6 )
~~~\..t.jnte[Co.~t~:,1 ± T',O.
.H, 12)
97. 'lx4
3
'
43. [-1,0];--0.900.
l'' r+cr
:1
\.
<
,.
,'-'
; 2
47. 8x + 5'+3x. _ 2
..
....
.59. (a) -421"
61., (a)
(b)
,,'
..
~~
37. 0, even ';':ulti~iicity;
119.N~~t",~e~~"
(d) No
Y'."""
)
0
~
.
~
':35, 0,
f, odd
±-!3,
odd
multipllelty
multiplicity
..
63, (a)
•
• .
~ymp!ote:x = 0
+1)(" - 4)
.
.,'.,
.':
r-
~,'
121. ,,-itllercep"·.(':'i;d)
Answers wllf vary..
(b) (x +1); (x - 4)
(d)
(e)
..
~(-'.~1 .
y.intor'cep!: (0;'2).
'. ;.
Yeltical' ••
-:
J
(').~,
..1'
,
.
.-3
'.,
...
:-10.
"-
,55,,..6.t-.21;'.. 67,·1.1'+ 3i,
~
40
.r" .
+ 651...c'
"
73,
-4 -. 46/;
69,3 ,F71'
..
~
75 '. IT
)0
+ iil .
",;~:.
,,;.,,:.;:_~·~;t'\, : ;:-,.;'~~::.~~~r::
..; , ",\ ....~':,..~
"
.r':
ympl.to: "'.'C'
}j~ri"~~t.i
~~Y~l'~oi~:
., ':"1
""':'" ...•.;, i' .• -,.
,,~:,
.
..
,;',N~'Il~.b o~o4glti symmetry' :.';" .
1«) :' (x+ ~)(x-: 4)(" +2)(>::;-3)
(d) -'2, -1,'3, 4
-t-I~j
~
. .~,-
~;
.
r
l'.
(x + J)
(e)· Answers will.vary.
,
....
"
~ = 1·
":',
(b)-[
3
:
_.
.
,,'<.
sYlllrIJe"1'
Vertical,
~'"
-f--,
,
-I' ~
-4
,
_
};!7, 1(.) ='1(. + t)'.~l!.
.~.
..
1Iodzoll,lal!asymptote:
.
~.
39. (a) nlsosto.fue left,.falia to the right
-"5
~~~
=·0 ..,.: " v;
=::'2, x 4'I 2 .
(e)
33, -7,~; odd multiplicity
~,:
-.I4T'
~r- x.intetcepj~:'.(±-.-2-'-"
V"~7),
~9. Palls 10 the leJ't;·fall. to the right
.'
'.f
.
55,2<'- llx --:6
(bf-9----
Answers.willvary,'
j(')=·;(,+7)(x
(d) -7, :"1,4
~',
...•.
It',
-10·
,~;~,:.
,
k~" VcrL-e);: (-f, -~)
y..,. (~) Yes
(e)
:,~.,'
31. Rises to the left, rises to...the right
.
117. V"ti~"i ::SYIl1~t~te9:
~
.
.
8
53.6x' +.~x' :",llx -:,4:-.:;;::t,
(b)
,,:':"-3' ')
H~rjzOJ;I.r.,y;"plole:'y
-: 3i +- 2·,:·x' + 2
57, (a) Yes
"
115. Yertlc.l asym~tot~;
1
",
.,";;
99. 12,:1:1
'103. q,I''':'~lf(x)=*-'l)'
111. Domsin; 011fei\l nurnbers r '" "' ~2 .
113. ·D~m.in: ,,11reel number x >to 6,4-
49. 5x.+2
.
51:.x'
'.
95, .~4. 3'
)4'" + 17,' - 42x -l- ~4
-:-
109. A'U7Jerg WiJl1UY,'
45. [-1,0], [I, 2J; ~. -O.200.~1.772
'
"
"81' -4, .,:1:21
it, :I.:'~,~!:
±12~,.±·h ::.I:tl ±Q:.I
2.
~07. Tw~.r n·op~'ltl"o.'e81 te,o~'''~l1';neg,[yo re;! '
27.
3
8,1
:1:15,
81.1::1: 31
105. -4.:2 ~ 3i; g(x) =' ex -I---4)'J" ., 2 - 30(x -
~ . ~.7 .'
~.'
--;1'
1~1;-~,t.2±i
.'
2.l
·8S,
=!:11 ±:3,.±5,
'79., ~
- 91, ·-1.:-::~:6
.:.'-:93, 1,8
•
~.
~o x-Intercept
"
= 50, y = 50
,<
-t::-=t-ll r-i-H-:
."
.:
·X
'89.
.J .
-1-
~~:~. ~
. '..
~M"'~Icx: (1, 3} . ".
\j)i'~'
83.0,2
A = 100>: -x'
(e)
-AI
77:*'-
(d)
100-x
'
I
(b) -3,0,.1.
(e) Answers will vary.
(b) y-=
25,
'lr
~
-1
10
'.
Exercises and Tests
1091 units'
,
"
..
,
12
Answers to Odd-Numbered
41: (a) Rises to the rigbt, rise. to U,• .Jeft
)
0
23.
<
IS'"
I
h(.) = x
+ ~y+
F.
I
A126
~r: "-"'0'
x-intercepts: (-4±.JG,0)
.A125
I, -ffi
Vertex: (x-intercepts:
~},!-;
'i,lS,
,.--.v
"~,,,~,/
Answers to Odd-Numbered
(o.:n .I(
~-~;~~-~:
~.. ~~-- ~.~.
,>
. :':i;:;=i~
!AT~·;::
I, .
i~r::
,
~J~i'
(11
3• Intercept;
\~l
"1"
Exercises and Tests
()0, 0
131. Domain: all real numbers
y-axis symmetry
Slant asymptote: y = 2x.
~:i~:f
I~!~
'.
<
Answers to Odd·Numbered
;'h~
Al27
A128
"
"~Il1jJtot."y ~ 1
HorizOlll~
,p,~
,",
I'I
I
:"
~~i:
~m.~ ----~. ----'~'r? ...) -l
-1
(0.OJ' •
li'f
.,
1',~
. ,
(a)
133. Domaln: all real numbers .x •• - 2
. bl'
iJ't //.
j
I:"
++-1
-11
1<\0)
~;1(.;~~::t jf---:'-l--J4-.>'
·'.1
~·i.
I;;;
,
~f.27, Intercept
j
"
,:
.. "~
,
,
(0,0)'
.
~ij
11I.,.1"
~;~)~
2.y ~'ex:;- 3)'- 6' , '"
3, (a).50 feet.· (\Ji 61,6 feet .
:,
,
,:::1'-6
~~LL:'fl\T"3T
...
.. Area
5.3x+-,.
,x -+ 1
':(4, 14)
6"j(~J ;(4~-
esx
.
'I-_.
'x-
4
,
'= u"
Iwir
Horizontal asy,;"ptote: ~ = 0
~t
7. (a) -'g
9,.,-2,
(c) 4 < x < cc
..
:
'E]~O
,'
+ SL(b)
L :)0.
13,1ex)
14,
"!
,
~j.', ~
7
8, 2 - / .
11. 2, -'1, ±2i
:t1, -~
.' ,
-,
'.0
!
'= (0,1)
(-.,Il";O)
9,48 inches x 9,48 inches
}"$'
:' :,);-,
~
A
139,
;+~
B
.
ABC
W,':;+;;+
(;ll'IO) "
-?- -1.,.
x-5
·:..1
~l
-:
.
'!
'l~'i~
~•.•
'
,W~
as,ml;~ot.:;. ~ ~,+:\ .
:; ; ,
'~;f~', 3""
.,:, 1
.~~~
~8,;;.-:-!X '- ;., "
.:', "'~\~
f.9.'i){
. 'I, "
.
-l-
;i}{i
'{.,ii.
:!.,~rl
5 "',1
1".
','
, (O)"1(.t) •.••'..;,(r:·~3)~1,1(.,1."';;";'x'I-· 8.x"1- '1
" . ~
..: '. .
.
".
.,..
'.
3. AI1~WC11wll~ ~.[y,
.,
'5. ea) and (bW '" ";~1 -I- 5";:"'4
I
'
.
'j,
,~~J:
. ;j!~4:
1~1
.\21
7:':'~/~'~Fr~'~:~~
".'~~~':I-'.:'1 ,:.r~
-I-
,;;:~.;~.
!;~y
9, (0) ili. (0) II (c) Iv .(d) I·'· ;
..
":'
.
,',
, ,::.,,
'l'c~~
11. Ca):As: lal 'Increases, tlre grnl;);"b~c~l;io,j: wlder, md
, "':dec!e'ues.,II,lo '~II»l\' bcc6i~es, llo.rrbwci., Fat', ~ :<;.... O~;!
" 'graplt)~ fOiJ'!'ted 11tIho,lx:a~i{;~';';L:':':;;~-/ : .'
'?J~
J
,'"
'I'
'c.n(~l=~~'2)~'
":",5)=;>-:U
x'·',.~ ."
:" _..... : .•.
.
+ 28x' - 30x
=x·~.6x' + 16J:"- 24x+ J6
~"','
,,!.
.'
1)(x -.A)(x -t- ,/3);
12. j(x) = x~':'" 9x'
Cd)
..JI%
';.~t~!jj~~~~i\··1
.' '1,
!, ±../3
Real zeros:
, a'~(2X+:7)
.. x-4
Vertical asymptotes: x
If
"'IV
;, Pro.~[~J.~Sot~,i~lg~,
(pa~e
","'I
4x +.l4
.. ':"x=--·,:x - 4
11i~)~
it.-
-5.,
(x - 4)Cy.- 4) ='30
,,,In:t.
-.: .'
'1: :~.'
-J.
(b)
..',~
}I
I
,~9·A~h;;;~,{~.! ~:/;f~~~:~
'1:~/:"':~1
">",':" .
j
-a-
_•.
Origin symmetry ,
'::'11 :-',/
17. ;t' -.2 -;-~
.~~-.,.II
11(\.
-4 -1
~~.
t#:
.
,Sl.~t
I
~jr.,1~29,Intercept:" (0, 0)
~~'.
lhree h~f units 10 ihe right
,\
Hotiz.nt~l·syrnp!ot~: y.= O.
16:·,
"3"
....•-+-<
'--4
in the-u-axls followed' by, a vertical
translation of.two units upward·.
, (b) .Hori~onlallra'nslaUon·of
- .••• (
J .
r.\li:~
y:~;.:
~,:e')'Refl;eli~n
', ~
I
·1
;;0,'
. .4" Rise, ~o.the lefl,-f.lIs l~ ihe~~Ighl
HOlizont~l'n~ymptote:y
M~!i'
-.
14
l
~~i
'11"~J
'j'
,,_.:,,~,O\;
~ O·
cha~t~iTe~('.(pag~1'g1)
H
'.~~~
J'= -,1
;~:~.
,~[>[::,'"
°
135. As x increases, the.cost.approaches !!le horlzonul asymptote.c ::i·.O.S;1'he,ave.rage costperunit is $0.50;
,137. Ca)
';
. 1M:
x' .,..-...
149, --+---.
.. ~> + L (x' + 1)2:,
+1
155:Fo~rth degree',
CiAd
-,.
y,axis symmelry"
AI,,,
3x '
8(x,- ~)
,.
-
.' "f!ori,oJlJ<ll1ymptote:
x' +"lx - 8 = 0' .
0:>+x+5'"
(c) x' +'4
·,;" .... ·1
,
! i!!I\'
l~1f
(0)
, . Vertical asymptote: x = ~2·
.Slant asymptote •.y ~ x + 1
..
.,ymPto.1e! y ": c.
Horizonul
3)
9 •
153,. Answ~~s will vary. ~0r example:
'''r
t,11t
J,i;,
145. .Lt- --.~-8(x + 5)
zeros, 'and complex zeros occur In cOlljupate pairs. ~
4'.,
Orlgln ",symmetry
25
·x -
,g",
Exercises and Tests
151. Fa1se.~A fourth-degree polynomial can h~ve at ~ost four
lii{~
r;j25, Intercep; ,(0, 0)
'"
\1:;\1
4
-x + 4:
147 - ----, 2. x:,~ \' ..'"x'·
a-
~~i\',
'3
143, --'. x +2
1('
M,l;
'jJlo
L(~
Answers to 'Odd-Nurnbered
J
s
"
(Iii
;/"sjb! j~~r~a~:",ill0'g~;Phb~'~~rii~•. ~j(ic;,I,d ,1:lt
"decreases, llre grfljJl1becomes ~R1,:r.?\;V~I. ~~r~ >. ~!;
graph ls Iransi.ted \0. tberlghi; ;f7.oI·'b.< .a; the
Iefleet'd.ID 1l10.:c·~~1'
ti'ns!.t'~ to liloJ~j\f?l
"
-~
.. ,
,.. .
:""d'I'.
,!;.
..
gl!~!\!
','"
,.' !\Ib··r
'):'(W'r.
':f,
",.'
, :/!I,,:'
-,
':.
"; ..
:'
"\"
.'.',t~~;~,~"'::
."
'~1II
..1"
A154
Answers to Odd-Numbered Exercises and Test'
-,1
m'f -l··'fee
"''T
<t.
•.•
71.
Y
$
1
:j
'.
"~~.
29. 'IU( -~)
.
Exercises
~eVlew
:1. O.5.radian
:?T:
3
.
..
(page' 344)
'.
¥
. .+.
+
'.
".,
.
.
412
5ffi
co. = 41
' . 4
.
Ian 0 = -5
.'
.'.
•
It
250 •- 470
..
0',
1. ../3)
25
'"
--:n .
~
~~i
",,'
-~
(page 348 )
"""
(b) Hir
"
.
4'
4 ....
'~"'13
I'"
,,-', . :~,j,.'
,--,'
'.3:
.
~;
•
t
)
=
'. '"
; Vi
.oos495':=:-'2'
•.
.
.."
e ~ i'
cscf
3 JI3
e = --.
cas e
-.
2.fi3
= -- 13
.
~
,~
. cotf
:= ~
3
.
.....
1
:1 ~III.
I
..
'
I,.
.
'"Fo, ~
h
.
se <7'
-,
:~_ ~
,,:"""'''r''
.... ;"
'3,
.
'3 --113 .
.., t.·
sec'@··'·2---.-..seee-'
'
_
.: .,','.,:;,
. . i""
..
,.,.,".
..
"
.
'"
81.3.24
L' .
~:?
: .:.:,
I
.
-YI3
. 99;·
.
:~'~'.':
0__
tan495:-1.
~ -2'
~s>:
:=
.,
..
....
.
. .:
.
"
;.t..
'n'
"
".'
2'
.,." ....•.
w--~_:jl3'-
m
sin
97.
1.
.(-240')..;,.""../3....
I''''
. ..
l~~;77~anO'i6:·'79.b,ri6
(c) 225°
.1;; ..
cOS-,=:
~[}5. sln{-240').=Tieos(-240)
.. ~:.
4, Fo,.,!) ~
_ 3-rr'q
1
"
~i
"_
. .
2:"
..':~."
,
Y'
I
··1·
to
-; (an- -.....;3
2
3
'.
1
7"")~ ./3. cos(_1!!
=.
~~:
'"i\\j
<,:,
-tr
3
;.~i;!
15
I
'
A
.
A"
1\,(:
.
.3
.~kl...
If?3. SIU495.'
.iNk
':~,
''t,;
'95.
.':'~.~"
.'
~r::(.~~)~;~~.:
'I'"
,1»; . (
..,,'.'
4
.
,2! = _"
~,;\~.9'sm3
2'.
".,,,,
cotO=-
-
5
:.J,
, ''';;~l
15
.
·i'l·
53. 71.3'meterf.;t".,:~
e = ../24T
9=
1/j~
'(.~~;
CSC/)=-.-
',ee
4
Test
'1. (a)
cot 0 =
../24T
;',
. ..
~
.
sffi·
.
si..
,!;?
IS·
l
··.ii!~
: y'.",":,
:M11
''''''''''
.;"4'
( )
;.> ,,':
>:. ..: ....
.....
tan9='-~
4-%\lW~;:2ffi
4
'15'
93,
-z
15'
.,,'
(b) 264 cycles per second'
.J.1
secO =
d../i3
91, (.) y =J.:~ip528'11;<.
3·
,iit.;
'241
-/3
(_...2!)
~apter
.
.'.
15../241.
57..
sln9=--..... \ ' 241
~,4..im
.••.••••
.~~..
e = _./55
kG7. Sin 6. =":-s.
":~;::r':::::r~J
=
-----u.-
'.~Iril
(d)
55
cot
~~~;~ cot 6. =
~f..!J
..
=21
"
8./55
aecf _. _
.. 5::;rr ..
"rJ.<;:..
[
..
.csc 9. ='3.
3../'i
.51., 3.67'
:.. cscs
tan 0=:"'"
<
\~.
,'Nlhi
.../'i
87•
8
5
6../IT
/l,>-,
,1i1!1i.
... '
55
.
~~~. csc
~Z~'
(c) --
. 49,0.56.
o'';f
'e~:o
;0'",
.- .....•
.
..~..'
1~. 128.57. .15 •. -200.54
11. 8.37.16'
19. -0.5890
21. (a) 66~,"r.dian,permlnute
mInute
(b) 400,,-incbuper
23 (
47. 0.65
."< "55.'in
0 = __
ceo s -.-1:'1
I~~ ...
·:it~
I
='4.
.JIT
",.«.
~l
·,";4'~~!;,'
'3-'.'
tan 0 = _ 3./55
6'
~;nl~1
':Q~,r
;;~{%
4../i3
(b) .. 4
ccs f
~N{.tan
)'li\~
~.h
~.
-If
~65.
./55
.. ccs e =.._ -a-'
-6-
..'5" '.'
Cl
~L
"",,!
-/3
.JIT
_.j3
cot8- 3
4"" .
Ji5
45 (a) •
4
,
'i'i:\ii.~
secO~2
..~
1
"P~
,;t~1j
cse9=-3-
.'
2../'i
43. (a> 3.', (b):--y
(0)
• -tiO
8 - 21
2-/3'
"cOb.
5.
_5
:cotO ,"7 '4
.".
.
,~",r
;,fiM.
,:
•
-a-
,i)I:..
e = ~ r:
85.
..
l' .
'socO=07'
.'
,"
.
4
cot 6
't.) ..
~~)~~~~
e5C,o:".~;:
.' ,
li!.?).slo 0 --:-.
,y
=;:!!!.
esc 0
17
,WH
·oj~!i"i:'
Ian 0 =
coss
J!~'!!
1!~I~'JI1:
cos
17
=.Jf!-
l~i!; tan 0 = 4
'1tii.'I.:.
4:t sin
\!,41. SUI 0
'Ii'~j~.
"':l.\'i."
2~;!,
= 4.jl7
'~.,
:liv~!\
.-/3
=T
..
+
83.
1
cot 8·-'-0.1
;!;t .
i~
(:.~
.;.,~l!
--d2.".
.../41
-lj<.
3!.'~~·'*:1
1
6.
.;~?
'.it.ll.
'37. 3.24
r
11.·'
430 • -290
6
8
.
~ _101J"
3t
3
9..,
f'
39· sin 0 = ~ ""
•
.~ _51r
:4"~' 4
.
.35. -75.31
. 7.,
. .
=
.
3. 4.5 radian,
.'
,"2]~~
. 17,"'
.. 717'.
·.33.Sin(~-)=sin-=·~-
-
•
.
cot(
= ..J3
3.
.
see(--)=-2
. 3
2·
. 2?T .
= --
esc( --)
31. Sinl~"-sin~
r
5. .
L
= --
tan(--)
2./3
e~
seC.e"", -9.
k.!.lae~-M
'1/""
'~f& tan8--9
:"
2'fT
csc
~'•.
~I
:~{!t
J.3
c,ot7=
-/3
..;~
"i:
3
7'fT
cos(-~)=.--
....
'. .
6
tr .
I~'
--4
'-'"
.
'"
tan-p=·3··....
-I .
. '. '.
•
see?.!!. = _2.j3
2
7'11" ,,3
j
•
-I
• '
-.
6
.
.
.
.J3
cos!:!!. == _
A1S5
Answers to Odd-N umbered ~xercl,e, ,and Tell, .
13
2
CDS
e=
.. . .
2.JE"
...!..--
.13
.'.'
l
_ .:...JTI.
.....
.
'
.':=:'.~.
cot.e'
3
: