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section 2_4 homework - 190 CHAPTER 2 Functions 1~1€l W...

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Unformatted text preview: 190 CHAPTER 2 Functions 1~1€l W Suppose the graph of f is given. Describe how the graph of each function can he obtained from the graph of f. L(my=fu)w5 m)y=f©“5} 2. (a)ymf{x+7) (b) y=f(x)+7 3.(a)ymf(x+%) (b) y=f{x)+-§- 4. (a) y 2: Mflx) (b) y 2 fWC) 5. (a) y 3 -2f(x) (b) m W305) 6. (a) y = —f(x) + 5 (b) y m 3W) — 5 7.(a)y:f(x—4}'+% (b}y*f{x+4)-% swmy=wu+mu2 acyzfiu—m+2 9. (a) y = mac) - (b) y = 16x) 10. (a) y = —f{2x) (b) y = fax) “ 1 11-16 E The graphs of 3° and g are given. Find a formula for the function g. a)y=% “(CHWJ $9. [The graph " functions. 17—18 H The graph of y 3 fix) is given. Match each equation j with its graph. ' 17. (a) y 3 fix w 4) (c) y = Zflx —i~ 6} (b) y 3 f{x)‘+ 3 (d) y E “fwd ® +-"+i ! m t (x) (b) y : *f(x + 4) (d) y = f{"x) a graph of f is given. Sketch the graphs of the following fictions. is graph of g is given. Sketch tho graphs of the foliowing notions. to the graph off to sketch the granhs of the foltowing actions. .. W _1 x (mymxwi l x-"3 = (iv)ym1~t~ SECTIGN 2.4 Transformations of Functions 191 22. (a) Sketch the graph of g(x) = “3/ch by plotting points. (b) Use the graph of g to sketch the graphs of the following functions. (t)y=\3/£T“§ (iii)y=1-\3/JE (it) ymx3/x+2+2 (iv) y22NZ/E 23—26 3 Explain how the graph of g is obtained from the graph of f. 23. (a) f(x) = x2, g(x) : (x + 2}2 (5) fix} 5 x2: 9'06} m X: "i" 2 24. (a) fix) w x3, g{x) = (A: ~ £83 (13) fix) 2 x3, g(x) = x3 — 4 25. (a) fix) = V22, 9(x) : 2%? (is) ax) = Vi, an at “2 26- (a) fix IXI, 90?) z 3i?” +1 {b} fix) L" WI» 90‘) = “Hi 1| 3E 27—32 E A function f is given, and the indicated transforma— tions are‘apolied to its graph (in the given order). Write the equation for the final transfonned graph. 27. f(x) = x2; shift upward 3 units and shift 2 units to the right 28. fix) m“- x3; shift downward 1 unit and shift 4 units to the 26ft 29. fix) m V}; shift 3 units to the left, stretch verticatty by a factor of 5, and reflect in the x~axis 39. f(x) =_ 6%; reflect in the y—axis, shrink verticaliy by a fac— tor of and shift upward i unit 31. f(x) 2 [x l ; shift to the righté unit, shrink verticaily by a factor of 0.1, and shift downward 2 units 32. fix) a Ix i ; shift to the ieft 1 unit, stretch vertically by a factor of 3, and shift upward 10 units 33—48 3 Sketch the graph of the fonction, not by plotting points,b12tby starting with the graph of a standard function and applying transformations. 33. fix) a (x»~~2)2 34. fix) =(x+7)2 35. f(x)m m(x-i-1)2 36. _f(;c)m1wx2 37. fix) =x3+2 38. fix) m "x3 39.y=t+\/;Tc 40.y=2-\/£Tt 41.ym% x+4m3 42.y=3_2(x-1)2 43.ym5+{x+3)2 44.y:%x3-1 45.y=lxi-I 46.y=ix-1| 47.y=1x+2i+2 48.y=2—|xl ea BE 192 CHAPTER 2 Funafions 4952 e Graph the functions on the same screen using the SS. given viewing rectangle. How is each graph reiateti to the graph in part (a)? 49. Viewing rectangle {—8, 8] by {"2, 8] (a)y=\i€c (b)y=\/“x+5 (c)y:2\“/£"3¥"§ (d)y=4+2m 56. Viewing rectangle [w 8, 8} by [w 6, 6] (flymixl (blyaflxl (c) y=“3lx! (diymm3ixm5i . . 57—58 m Use the graph of fix) : described on pages . " , — , 4 . . . 51 Viewmg ricwflglfi 4 63b“ 4 I} 6 162—163 to graph the indicated fonctxon. (£1)ny (b)y='3-x (c) y 3 Mix“ {6) y = ~i(x — 4f 57- y e ilsz 58- y = iixl 52’ Vifiwgng refmngiehfi’ GJbflmdi’ 4] 1 {fig 59. If fix) = V 2): - x2, graph the following functions inthfi (a) E. W (b) : __ viewing rectangiefmi S] by {"4, 4]. How is each graph 5" y V32 y Vx + 3 iated to the graphin past (a)? 1 ___1___ - 3 (a) y = f(x) 53) y 2 far) (0) y m fiixi i“) “W (“Nix/m 53. The graph of g is given. Use it to graph each of the foilowing functions. (a) y = we o) y m nix) fig 60. If flx} m V 2x - x2, graph the following functions in $11" viewing rectangle [-5, 5} by [-4, 4]. How is each graph reiated to the gragh in part (a)? (a) y 2 fix) 0)) y m first) (c) y e —f(- (d) y = f{-2x} (e) y '—"—"’ f(-—%x) 61w68 m Determine whether the function f is even, odd, or neither. If f isieven or odd, use symmetry to sketch its graph. 6i. f(x} = )6"2 62. f(x) = x'3 63. fix) m x2 + x 64. flx) m x4 — 4x7” 65. fix) = x3 — x 66. fix) 2 3x3 + 2x2 + 1 54. The graph of h is given. Use it to graph each of the following functions. - 57‘ fix) = 1 .— fi 63_ fix} 2 x 4;“ "1m x (a) y = hex) (b) y w hex) 69. The graphs offlx) = x2 —— ti and g(x} = 1x2 - 41 are shown. ExpEain how the graph of g is obtained from the graph of f. 55—56 The gragh of a function éefined for x a 0 is given. Complete the graph for x < O to make (a) an even function (h) an odd function e grape of f(x} =-" x4 - 4x2 is shown. Use this graph to ' sketch the graph of g(x) 5 ix” m 4x2 \: ‘1 re“ bed'on pages ' |4xmx2| 31 we 3 '3 V ll >1 w A a. V ‘3‘ M v li V g functions in v is each graph (‘3) y m "f( ‘_ ates Growth The annual sales of a certain company ' an be modeleé by the function fir) = 4 + 0.03:2, where represents years since 1990 and f(r) is measured in millions of dollars. Ia) What shifting and shrinking operations must be per- fortneti on the function y m r2 to obtain the function y e ftr)? ) Suppose you want t to represent years since 2000 in- ' stead of 1990. What transformation wouid you have to 5 even, out}, or ketch its graph the new function y m g(r) that results from this trans- formation. apply to the function y w fit) to accomplish this? Write SECTlON 2.5 Quadratic Functions; Maximo end Minima 193 '74. Changing Temperature Scaies The temperature on a certain afternoon is modeled by the function 60‘) m it? 43 2 where t represents hours after 12 noon (0 E r S 6). and C is measured in °C. (a) What shifting and shrinking operations must be per- formed on the function y x r2 to obtain the function y = CO)? (13) Suppose you want to measure the temperature in “F instead. Mat transformation would you have to apply to the function y m C(13) to accomplish this? (Use the fact that the relationship between Celsius and Fahrenheit degrees is given by F 3 2C ~l~ 32.)W1ite the new function y m F{t) that results from this transformation. Discovery e Discussion 75. 76. 77. Sums of Even and Odd Functions If f and g are both even functions, is f + g necessarily even? If both are odd, is their sum necessariiy odd? What can you say about the sum if one is odd and one is even? In each case, prove your answer. Products of Evan and Odd Functions Answer the same questions as in Exercise 75, except this time consider the product of f and 9 instead of the sum. Evan and Odd Power Functions What must be true about the integer n if the function f(x) m x" is an even function? If it is an odd function? Why do you think the names “even” and “odd” were chosen for these function properties? sunerreas; "anagram an new ' A maximum or minimum value of a function is the largest or smallest value of the function on an interval. For a function that represents the profit in a business, we would be interested in the maximum value; for a function that represents the amount of material to be used in a manufacturing process, we would be interested in the min— imum vaiue. In this section we learn how to find the maximum and minimum values of quadratic and other functions. ...
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This note was uploaded on 10/07/2009 for the course MATH 150 taught by Professor Unknown during the Spring '06 term at Ohio State.

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section 2_4 homework - 190 CHAPTER 2 Functions 1~1€l W...

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