284 CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS 56. P(x) = -x* + 2x' + 3x² – 4x – 4 56. P(x) = -x+ 2x+ (In factored form, P(x) = -(x - 2)-(x + 1)².) 35. P(x) = -xr + 5x-1: a =0.1, b = 0.2 57. P(x) = -x + 3x' + x² - 3x 36. P(x) = -x-21+x-3; a= -2.8, b = -2.7 In Exercises 37 to 44, determine the x-intercepts of the graph of P. For each x-intercept, use the Even and Odd Powers of (x - c) Theorem to determine whether the graph of P crosses the x-axis or intersects but does not cross the x-axis. 58. P(x) =x* + x³ – 2x² – x + %3D 3).) (In factored form, P(x) = 7(x– 1)*(x + 1)( + 59. P(x) = x – x* – 5x' + xr? + 8x + 4 (In factored form, P(x) = (x + 1)*(x – 2)2) %3D 37. P(x) = (x – 1)(x + 1)(x – 3) 38. P(x) = (x + 2)(x – 6)² %3D 60. P(x) = 2x – 3x* – 4x' + 3x² + 2r In Exercises 61 to 66, use translation, reflection, or both concepts to explain how the graph of P can be used to 39. P(x) = x(x – 5)(x – 3) 40. P(x) = -(2x – 8)(x - 7)² produce the graph of Q. Q(x) = x' + x + 2 41. P(x) = x² (x – 15)(2x – 7)² 61. P(x) = x + x; 42. P(x) = x(x + 4)(x – 5)² 62. P(x) = x*; Q(x) = x – 3 43. P(x) = x – 6x² + 9x 63. P(x) = x*: Q(x) = (x – 1)* 44. P(x) = x + 3x + 4x2 64. P(x) = x'; Qx) = (x + 3) %3D 65. P(x) = x; Q(x) = -(x – 2) + 3 In Exercises 45 to 60, sketch the graph of the polynomial function. Do not use a graphing utility. 66. P(x) = x°; Q(x) = (x + 4)6 – 5 45. P(x) = x –- x² – 2x A Medication Level Pseudoephedrine hydrochloride is an allergy medication. The function 67. 46. P(x) = x + 2x² – 3x %3D 47. P(x) = -xr - 2x + 5x + 6 (In factored form, P(x) = -(x+ 3)(x + 1)(x - 2).) L(t) = 0.03t + 0.4r – 7.3t + 23.1t 48. P(x) = -xr – 3x² + x + 3 (In factored form, P(x) = -(x + 3)(x + 1)(x – 1).) where 0
284 CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS 56. P(x) = -x* + 2x' + 3x² – 4x – 4 56. P(x) = -x+ 2x+ (In factored form, P(x) = -(x - 2)-(x + 1)².) 35. P(x) = -xr + 5x-1: a =0.1, b = 0.2 57. P(x) = -x + 3x' + x² - 3x 36. P(x) = -x-21+x-3; a= -2.8, b = -2.7 In Exercises 37 to 44, determine the x-intercepts of the graph of P. For each x-intercept, use the Even and Odd Powers of (x - c) Theorem to determine whether the graph of P crosses the x-axis or intersects but does not cross the x-axis. 58. P(x) =x* + x³ – 2x² – x + %3D 3).) (In factored form, P(x) = 7(x– 1)*(x + 1)( + 59. P(x) = x – x* – 5x' + xr? + 8x + 4 (In factored form, P(x) = (x + 1)*(x – 2)2) %3D 37. P(x) = (x – 1)(x + 1)(x – 3) 38. P(x) = (x + 2)(x – 6)² %3D 60. P(x) = 2x – 3x* – 4x' + 3x² + 2r In Exercises 61 to 66, use translation, reflection, or both concepts to explain how the graph of P can be used to 39. P(x) = x(x – 5)(x – 3) 40. P(x) = -(2x – 8)(x - 7)² produce the graph of Q. Q(x) = x' + x + 2 41. P(x) = x² (x – 15)(2x – 7)² 61. P(x) = x + x; 42. P(x) = x(x + 4)(x – 5)² 62. P(x) = x*; Q(x) = x – 3 43. P(x) = x – 6x² + 9x 63. P(x) = x*: Q(x) = (x – 1)* 44. P(x) = x + 3x + 4x2 64. P(x) = x'; Qx) = (x + 3) %3D 65. P(x) = x; Q(x) = -(x – 2) + 3 In Exercises 45 to 60, sketch the graph of the polynomial function. Do not use a graphing utility. 66. P(x) = x°; Q(x) = (x + 4)6 – 5 45. P(x) = x –- x² – 2x A Medication Level Pseudoephedrine hydrochloride is an allergy medication. The function 67. 46. P(x) = x + 2x² – 3x %3D 47. P(x) = -xr - 2x + 5x + 6 (In factored form, P(x) = -(x+ 3)(x + 1)(x - 2).) L(t) = 0.03t + 0.4r – 7.3t + 23.1t 48. P(x) = -xr – 3x² + x + 3 (In factored form, P(x) = -(x + 3)(x + 1)(x – 1).) where 0
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Transcribed Image Text:284 CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS
56. P(x) = -x* + 2x' + 3x² – 4x – 4
56. P(x) = -x+ 2x+
(In factored form, P(x) = -(x - 2)-(x + 1)².)
35. P(x) = -xr
+ 5x-1: a =0.1, b = 0.2
57. P(x) = -x + 3x' + x² - 3x
36. P(x) = -x-21+x-3; a= -2.8, b = -2.7
In Exercises 37 to 44, determine the x-intercepts of the
graph of P. For each x-intercept, use the Even and Odd
Powers of (x - c) Theorem to determine whether the
graph of P crosses the x-axis or intersects but does not
cross the x-axis.
58. P(x) =x* + x³ – 2x² – x +
%3D
3).)
(In factored form, P(x) = 7(x– 1)*(x + 1)( +
59. P(x) = x – x* – 5x' + xr? + 8x + 4
(In factored form, P(x) = (x + 1)*(x – 2)2)
%3D
37. P(x) = (x – 1)(x + 1)(x – 3)
38. P(x) = (x + 2)(x – 6)²
%3D
60. P(x) = 2x – 3x* – 4x' + 3x² + 2r
In Exercises 61 to 66, use translation, reflection, or both
concepts to explain how the graph of P can be used to
39. P(x) = x(x – 5)(x – 3)
40. P(x) = -(2x – 8)(x - 7)²
produce the graph of Q.
Q(x) = x' + x + 2
41. P(x) = x² (x – 15)(2x – 7)²
61. P(x) = x + x;
42. P(x) = x(x + 4)(x – 5)²
62. P(x) = x*; Q(x) = x – 3
43. P(x) = x – 6x² + 9x
63. P(x) = x*: Q(x) = (x – 1)*
44. P(x) = x + 3x + 4x2
64. P(x) = x'; Qx) = (x + 3)
%3D
65. P(x) = x; Q(x) = -(x – 2) + 3
In Exercises 45 to 60, sketch the graph of the polynomial
function. Do not use a graphing utility.
66. P(x) = x°; Q(x) = (x + 4)6 – 5
45. P(x) = x –- x² – 2x
A Medication Level Pseudoephedrine hydrochloride is an
allergy medication. The function
67.
46. P(x) = x + 2x² – 3x
%3D
47. P(x) = -xr - 2x + 5x + 6
(In factored form, P(x) = -(x+ 3)(x + 1)(x - 2).)
L(t) = 0.03t + 0.4r – 7.3t + 23.1t
48. P(x) = -xr – 3x² + x + 3
(In factored form, P(x) = -(x + 3)(x + 1)(x – 1).)
where 0 <t< 5, models the level of pseudoephedrine hydro-
chloride, in milligrams, in the bloodstream of a patient
hours after 30 milligrams of the medication have been taken.
49. P(x) = x – 4x + 2x² + 4x – 3
(In factored form, P(x) = (x + 1)(x – 1)*(x – 3).)
a. Use a graphing utility and the function L(t) to determine
the maximum level of pseudoephedrine hydrochloride-
in the patient's bloodstream. Round your result to the
nearest 0.01 milligram.
%3D
50. P(x) = x – 6x + 8x²
51. P(x) = x + 6x + 5x - 12
(In factored form, P(x) = (x – 1)(x + 3)(x + 4).)
%3D
16
52. P(x) = -x + 4x² + x - 4
12
8 -
53. P(x) = -x + 7x - 6
%3D
54. P(x) = x – 6x² + 9x
(In factored form, P(x) = x(x – 3)².)
3
4
Time (in hours)
55. P(x) = -x' + 4x - 4x
(In factored form, P(x) = -x(x – 2)*.)
b. At what time t, to the nearest minute, is this maximum
level of pseudoephedrine hydrochloride reached?
68.
Profit A software company produces a computer game.
The company has determined that its profit P, in dollars,
from the manufacture and sale of x games is given by
Unless otherwise noted, all content on this page is Cengage Learning.
Pseudoephedrine hydrochloride
in the bloodstream (in milligrams)
20
4-
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