This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1011 will see" Exeticfieee: (.— 22 3 Sketch the graph of the function by ﬁrst making a table 'ygliles r ‘ I) 5 2. ﬂx) : "“3
1 .:f(x)ﬂ2x"_4 4. ﬁx) m6W3X
.f f(x)xwx+3, m3ﬁx$3
,le 535—131, 0$x$5
2
t" ZN 8.f{x)=x2—4
mx3~ 8 10. g(x) m4x2wx4
a x/x + 4 12. g{x) :2 vi”;
a m 1
.17.; 14.F(X)—x+4
=]2x§ 16.H(x)=x+ll
}rzx+x '18. G(x)=1xx
ﬁx): 5 _.._f{x)= szwm 20. new???
2
3‘ =35"; 23 g(x) “if; he graph of a function h is given.
a) Find h(2), hm), h(2), and h(3).
b) Find the éomain and range of h. he graph of a function g is given.
7'?) Finé 9V4), iii—2). 9(0). 9(2), and 9(4) SECTION 2.2 Graphs of Functions 25. Graphs of the functions f and g are given.
(21) Which is larger, f(0) or 9(0)?
{11) Which is larger, f(—3) or g(—3)?
(c) For which values of x is ﬁx} 3 g(x)? 26. The graph of a function f is given.
(a) Estimate HOS) to the nearest tenth.
(b) Estimate f(3) to the nearest tenth.
(c) Find all the numbers )5 in the domain of f for which ﬁx) 2 i. Iii
t
Kl "eat." m’ I'mII
a! . gig} muuunmlamu II" II “=I : g. .55; ' g
Elﬁn REE: iiiiiiiiiiaﬁiii
ﬁniiiiaiii I'll.
33553: x maulInn summitu am
V :55
ii!
iii:
5 i '
iiii
aa '
In
iii
ii!
iii
If E§ 27—36 a A function fis given. (3) Use a graphing caicuiator to draw the graph of f.
(1)) Find the domain and range of f from the graph. 27. ﬁx) w x W 1 28. f(x} = 2(x + 1)
29. 39(1) ""—* 4 39. f(x) = x2 31. ﬁx) = 4 — x2 32. ﬁx) 3 x2 ”h 4 33. ﬁx) = m 34. ﬁx) : .. 25 w x2
35. ﬁx) = VET—1 36. ﬁx) 2 WT? 37—50 3 Sketch the gragh of the piecewise deﬁned function. 0 ifx<2
37' ﬁx) .1 {1 ifxa2 167 1G8 CHAPTER 2 Functions 1 if x 531 53m54 5 The graph of a piecewise deﬁned function is given. .50 ﬂ Deten
33 f (x) = x + i if x > I. ﬁnd a formuia for the function in the indicated form. is, Sign”: ﬂ
3 if x < 2 35—1 ifx22 ifx< 2
ﬂ iwaExﬁ
ifx>2 40. f8) = {5 ifx a *2
41. ﬂit) 3 { 42. for) x w1 ifx<w1 .
43.j(x): 1 ifwli—xﬁl *fxﬁ—l
W1 ifx>1 m IfW1<xS
ifx>2
1 ifx<~1
44.f(x): if—lsxgl
i ifx>1
_ 2 If x g *1 5556 5 Determine whether the curve is the graph of afimctio
45. ﬁx) “‘ x2 1fx> w] ofx.
55. (a) (b)
' )‘A
1x2 foSZ
46' ﬁx} 5 {x ifx > 2
. W 0 iflxl 52 0 x
ammo—{3 1f1xi>2
48' f(x)"{1 Jim >1 4 ifx<w2 0 x
49. f(x) = x2 ifwZiixsz , W
—x+6 ifx>2 50.f(x): 9—x2 if0<x£3
x m 3 ifx > 3
0 x
51—52 33 Use a graphing dewce to draw the graph of the piecewise deﬁned function. (See the margin note on page 162.} {c)' y (d)
x + 2 ifx S ""1 ‘
5}" ﬁx) " {x2 if): > —1 y
2 O x
2x~x ifx>1
52, .7: n is given. '57469 e Deterhnine whether the curve is the graph of a function 4' If i€ gs, state the domain anti range of the function. r.
.57. {‘72 H Determine whether the eguation (ieﬁnes y as a function .fofx. (See Exampie 10.) $1.):2l2y24 62.3x+7y=2t
away? 64.x2~1~(y—1)2w4
§S.x+y2=9 66.x2+ym9
:_7.x2y+ym 68.\/;c+y=i2
69.2ixi+y=0 70. 2x+y=0
_il.x=y3 72. xzy“ 3—78 It A family of functions is givers. In parts (a) and
)graph all the given members of the famiiy in the viewing (33) c a 0, ~2. —4, ~6; [—5, 5] by [m10, 10}
(E) How does the vaiue of c affect the graph?
fix) “7 (I * CY
(a) c m o, 1, 2, 3, (ms, 5]i)y[10, 10] '(b) c m 0,—1,w2,m3; [—5, 5]by[—10. 10} ' (0) How dees the value of c affect the graph?
S._f(x) m (x m 0}} (a) c 2 0,2,4, 6; [~10,10]by{—10,10} (b) c = 0, —2, —4, ~6; [10, 10] by [Mia 10} (0) How does the vaiue of 6 effect the graph? SECTION 2.2 Graphs of Functions 169 76. ﬁx} a (3352 (a) c = 1,31, 2, 4; {~~5,5]by[—10. 10] (b) c m1,w1,wi,— ; [—5,5}by{~10,10} (c) HOW does the value of 0 effect the graph?
'77. f(x) = xc (a) c =hié; i‘lr4ibY[“1a3i (b) c = 13,51; {m3,3]by[w2,2} (c) How does the value of c affect the graph?
73. ﬁx) m‘ l/x" (a) n "—m 1.3; [—3, 3}by{3, 3] (h) n = 2,4; [—3, 3] by{—3, 3] (c) How dees the value of rt affect the graph? 79~82 E Find a function Whose graph is the given curve.
79. The line segment joining the points (m2, 1} and (4, —6)
89. The line segment joining the points {—3, ~2) and (6. 3)
81. The top haif of the circle .752 + y2 m 9 82. The bottom half of the circle x2 + y? m 9 Applications 83. Weight Function The graph gives the weight of a certain
person as a function of age. Describe in werés how this
person’s weight has varied over time. What do you think
happened when this person was 30 years old? 200 Weight 150
(pounds) 100 501 10 20 30 40 50 60 70
Age (years) 84. Distance Function The graph gives a salesman’s dis
tance from his home as a function of time on a certain day.
Describe in words what the graph indicates about his travels
on this day. Distance
from home
(mites) 8AM. 10 NOON 2 4 6PM. Time (hours) 170 85. 86. 87. CHAPTER 2 Functions Hurdle Race Three runners compete in a EGOmeter hur~
dle race. The graph depicts the distance run as a function of
time for each runner. Describe in words what the graph telis
you about this race. Who won the race? Did each runner
ﬁnish the race? What do you think happened to runner B? y (m)
we 0 f 20 Ms) Power Consumption The ﬁgmre shows the power con
sumption in San Francisco for September 19, 1996 (P is
measured in megawatts; t is measured in hours starting at
midnight). (a) What was the power consumption at 6 A.M.? At 6 RM?
(b) When was the power consumption the lowest?
(c) When was the power consumption the highest? Pat/rm
800 600
400 200 ,, i . a ‘i W
E} 3 6 9 12 15 18 211(1)) Source: i’aciﬁc Gas & Electric Earthquake The graph shows the verticai acceleration
of the ground from the 1994 Northririge earthquake in Los
Angeies, as measured by a seismograph. (Here trepresents
the time in seconds.) (a) At what time I did the earthquake ﬁrst make noticeable
movements of the earth? (1)) At what time tdid the earthquake seem to end? (c) At what time twas the maximum intensity of the earth
quake reached? . a
(curls?)
20!} 50 0 t(s) Source: Calif. Dept. of
Mines and Geology gg 94. Graph of the Absolute Value of a Function 88. Utiiity Rates Westside Energy charges its electric
customers a base rate of $6.00 per month, plus 30¢ per '
kilowatthour (kWh) for the ﬁrst 300 kWh used and
6p per kWh for all usage over 300 kWh. Suppose a
customer uses x kWh of electricity in one month. (3) Express the monthly cost E as a function of x.
(1)) Graph the function E for 0 s x s 600. 89. Taxicab Function A taxi company charges $2.00 for
ﬁrst mile {or part of a mile) and 20 cents for each succeed
ing tenth of a Iniie (or part). Express the cost C (in dollars
of a ride as a function of the distance x traveled (in miles
for 0 < x < 2, and sketch the graph of this function. 90. Postage Rates The domestic postage rate for ﬁrst—clas‘l
letters Weighing 12 oz or less is 37 cents for the ﬁrst oun
(or less), plus 23 cents for each additional ounce (or part
an ounce). Express the postage P as a function of the weigh
x of a letter, with 0 < x S 12, and sketch the graph of thi
function. Discovery w Discussion 01. When Does 3 Graph Represent a Function? Fortv
integer n, the graph of the equation y m x" is the graph
of a function, namely ﬁx) : x”. Explain why the graph'cfi
x m 322 is not the graph of a function of x. Is the graph of
x = y3 the graph of a function of x? If so, of what funetic
of x is it the graph? Determine for what integers n the gm
of x m y" is the graph of a function of x. 92. Step Functions In Example 8 and Exercises 89 and V
we are given functions whose graphs consist of horizonla
line segments. Such functions are often called step '
functions, because their graphs look like stairs. Give
some other exampies of step functions that arise in
everyday life. 93. Stretched Step Functions Sketch graphs of the fu
tions f(x} = ﬂxﬁ, g(x) : EZxE, and h(x) m {13):}? on sop
graphs. How are the graphs rotated? If n is a positive in ,.
what does the graph of k(x} = {[an look like? (3} Draw the graphs of the functions ﬁx) 2 x2 + x '7
and g(x) m Ix2 i" x " 6 I. How are the graphs 0f
9 related? _
(b) Draw the graphs of the functions f(x) 3 x" W 6x23“
g(x) = ix“ r" 6x2 3. How are the graphs of f aﬂdg __
related?
(c) In general, if g(x} = 3 f(x)§, how are the graphs
off and 9 related? Draw graphs to illustrate your
answer. ...
View
Full Document
 Spring '06
 UNKNOWN
 Math

Click to edit the document details