section 2_1 homework

section 2_1 homework - Exercises Express the rule in...

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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) : 2|x 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 33-f(x)--x+1 34. fix)~»x_1 35. fix) a 3 — 5x + 4x2 36. fix) a x3 31-58 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, 9-1, 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 + 7x0-4 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 i-Iiight 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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section 2_1 homework - Exercises Express the rule in...

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