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Unformatted text preview: Exercises
Express the rule in function notation. (For example,
16}. game, then subttact 5” is exgressed as the function x2 * 5)
add 3, then multipiy iay 2
wide by 7, then s'ubtract 4 am this 1306 '(—u,h(2),hexh{x),Iii) SECTION 2‘1 What Is a Function? 17. ﬁx) 2 2x2 + 3x — 4; MD, f0), f(“2), f(\/§). f(x + 1), f{"I) 18. f(x) = x3 “ 4x2; Nam f(0)1f(1),f(“1)af(
19. ﬁx) : 2x W IE; ), ﬂxz) roman. f6). 112). ﬁx + i), ﬁzz + 2) 20 ﬁx) 3 iii; ice—2), f(1),f(0)f(5). more) 21m24 m Evaiuate the piecewise éeﬁned function at the indicated vaiues.
x2 if x < 6 2L JC(x)={1t+1 ii:an 3‘92), fiwl). f(0), f{1):f(2} 5 ifxEZ
22‘ fix) "” {2xw 3 ifx>2 f{—3), m3). 39(2). K3), f{5) x1+2x ifjcﬁ m1 23.1%): x if—1<x51
—I ifx > 1 31—4}, 11%), ate—1), ﬁe), K25)
3x ifx < 0 24.j(x)mx+1 ifOSxSQ
(JC""2)2 ifx>2 31—5), KO), f0): 19(2), f(5) 25—28 3 Use the function to evaiuate the indicated expressions and simpiify. 25. f{x) “w”: x2 +1; 3°06 + 2),f(x) + “2) 26. ﬁx) = 3x ~ 1; f(2x),2f(x)
27 fix) = x + 4; fog), we»? 28. me) = 6x w 18; ﬁg), 29—36 E Find ﬂat), f{a + h), and the difference quotient ﬂu + h)  ﬂu)
h 29. f(x} = 3x + 2 ,where h 3% (3. 155 30. ﬁx) m x2 + 1 156 CHAPTER 2 Functions
1
31. fee) m 5 32. ﬁx} m x + 1
x 2x
33f(x)x+1 34. fix)~»x_1
35. ﬁx) a 3 — 5x + 4x2 36. ﬁx) a x3
3158 E Find the domain of the function.
37. for) a 2x 38. ﬁx) w x2 + l
39. ﬁx) m 224:, —i SxWS
4O.f(x)=x2+1, OanS
1 1
41. ﬁx} —— x M 3 42. ﬁx) — 3x m 6
x + 2 x4
43. — 3:5": 44. — x2 + x m 6
45. ﬁx) m Vx, — 5 46. ﬂx) m 4x + 9
47. ﬁt) = V3 r — i 48. g{x) m V7 — 3x
49. h(x) "—“ V2x — 5 50. G{x) : Jr2 " 9
V2 + 3: V5:
51’ W) m “at? 52 W " 2x2 + x w:
53; g(x) x V4 x2 — 6x 54. g(x) e W — 2x — s
3 x2
55. = 56, f = m
ﬁx) x — 4 V5:
57m (“U2 58m x
. x = . ' x —
sz w 1 4 9 m— x2
Appiiea‘tions 59. Production Cost The cost C in dollars of oroducing
x yards of a certain fabric is given by the fonction C(x} = 1500 + 3x + 0.02;:2 + 00001;:3 (3) Find C(10) and C(100). (b) What do your answers in part (a) represent?
((2) Find C(O). {This number represents the ﬁxed costs.) 60. Area of a Sphere The surface area S of a sphere is a function of its radios r given by S{r} m 47rr2 (a) Find 5(2) and 5(3). (b) What do your answers in part (a) represent? 61. How Far Can You See? Due to the curvature of the earth, the maximum distance D that you can see from the 62. Torrieeiii's Law {A tank holds 50 gallons of water; in 63. Blood Flow As blood moves through a vein eras"! where r w 3960 mi is the radius of the earth and D measured in miIes. (a) Find D(0.1} and D(U.2).
(b) How far can you see from the observation deck
Toronto’s CN Tower, 1135 ft above the ground? (0) Commerciat aircraft ﬂy at an altitude of about 7
How far can the pilot see? drains from a teak at the bottom, causing the tank to
in 20 narrates. The tank drains faster when it is nearl
because the pressure on the leak is greater. Torriceil
Law gives the voiume of water remaining in the tank '
t minutes as I 2
V(r) —50(t M56) 0$t$20 (3) Find V(0) and V(20).
(b) What do your answers to part (a) represent?
((3) Make a table of values of V(t) for: = 0, 5, 10,1 its velocity 0 is greatest along the central axis and d H
as the distance r from the central axis increases (330 ﬁ‘ ﬁgere). The formula that gives u as a function of r iS' the law of laminar ﬂow. For an artery with radius 9
we have 0(r) rm 18,500(0.25 W r?) (3) Find u(0.1) and v{0.4).
(b) What do your answers to part (a) tail you alarmt
of blood in this artery? (c) Make a table of values of 0(r) for r = 0, 91, 0‘
0.4, 0.5. OSrSOJ {h is: Pupil Size When the brightness x of a light source is in—
. creased, the eye reacts by decreasing the radius R of the
pupil. The dependence of R on x is given by the function 13 + 7x04
R“) r \/ J (a) Find RU), R80}, and RUDD). 3n deck of {b} Make a table of vaiues of R(x}. ground?
' auger 7 mi . if water, whié tank to em neariy f
Porricclli’s _ _ . . .
' gs, Belatmtv According to the Theory of Relativrty, the
length L of an object is a function of its velocity u with
respect to an observer. For an object whose length at rest 5 20 is 10 m, the function is given by
’2
U
L a a 10 1 m m
( ) C.
sent?
} 51 :0, 15' 2 where c is the speed of light. (a) Find L(0.5€}, L(O.7Sc), and 1203.90). (b) How does the length of an obiect change as its velocity
increases? . 65. Income Tax In a certain country, income tax '1‘ is assessed
' according to the following function of income 2:: 0 if0 g x 5 10,000
1(1) 2 0.08:: if 10,000 < x 5: 20,000 1600 + 0.le if 20,000 <1 x I (a) and T(5,000), trance), and 195,000).
(b) What do your answers in part (21) represent? 67. nternet Purchases An Internet bookstore charges $15
1 shipping for orders under $100, but provides free shipping
: for orders of $100 or more. The cost C of an order is a func
_ tion of the total price at of the books purchased, given by
at +15 ifx< 100 CW = {x ifx a 100 ' a} Find cos), C(90), cues), and cans).
'70) What do your answers in part (a) represent?
Ccst of a Hotel Stay A hotel chain charges $75 each iIiight for the ﬁrst two nights and $50 for each additional night’s stay. The total cost Tis a function of the number
f nights x that a guest stays. a) Complete the expressicms in the following piecewise
defined function. ex)={ ion of r is Calida ifOExEZ
ifx>2 SECTION 2.1 What is a Function? 157 (1)) Find T{2), 7(3), and (c) What do your answers in part (b) represent? 69. Speeding Tickets In a certain state the maximum Speed
permitted on freeways is 65 mi/h and the minimum is 40.
The fine F for violating these limits is $35 for every mile
above the maximum or below the minimum. (a) Compiete the expressions in the foilowing piecewise
deﬁned function, where x is the speed at which you are driving.
ifG < x < 40
F(x)= if405x565
ifx > 65 (in) Find F{30), F{50), and F05).
(c) What do your answers in part (h) represent? 70. Height of Grass A home owner mews the iawn every
Wednesday afternoon. Sketch a rough graph of the height of
the grass as a function of time over the course of a four~
week period beginning on a Sunday. 71. Temperature Change You place a frozen pie in an oven
and bake it for an hour. Then you take it out and let it cool before eating it. Sketch a rough graph of the temperature of
the pie as a function of time. 72. Daily Temperature Change Temperature readings T
(in °F) were recorded every 2 hours from midnight to noon
in Atlanta, Georgia, on March 18, 1996. The time twas measured in hours from midnight. Sketchla rough graph
of T as a function of r. ...
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 Spring '06
 UNKNOWN
 Math

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