Section 3.3 Functions 189 73. 74. 4 4 8 8 –4 –8 –4 –8 x y 6 2 2 4 4 –2 –4 –2 –4 x y 75. x = 3y + 1 76. x = y - 6 77. y = |x + 3| +1 78. y = |5 - 2x| 79. x = (y - 4)2 80. x = (y + 7)2 81. x y 0 3 1 4 2 6 0 5 82. x y -7 3 0 4 2 4 5 5 Given the graph of each function, find the indicated values. 83. Find g(-3) for g(x). 84. Find g(8) for g(x). 4 2 8 –4 –6 –4 –2 –8 x y 2 4 4 8 –2 –8 –4 –4 x y 85. Find f (-3) for f (x). 86. Find f (1) for f (x). 6 2 2 4 4 –2 –4 –2 –4 x y 12 4 –4 –2 2 x 8 4 –4 y Use the given function to solve each problem. 87. Find f (0) if f (x) = 3x 2 - 4x + 5. 88. Find f (-2) if f (x) = 1 2 x 5 - 5x 4 + 3. 89. The estimated number of AIDS diagnoses can be modeled by the equation d(x) = 222x3 - 2712x2 + 9812x + 27,565, where x is the number of years after 2000. Find d(10) rounded to the nearest whole number and interpret. (Source: http://www.cdc.gov) 90. Use the function given in Exercise 89 to find d(13) rounded to the nearest whole number and interpret. (Source: http://www.cdc.gov) 91. The percentage of smokers among adults age 18 and over is modeled by the equation k (x) = -0.44x + 23.11, where x is the number of years after 2000. Find all x rounded to the nearest whole number such that k (x) = 20 and interpret. (Source: National Center for Health Statistics) 92. Use the function given in Exercise 91 to find all x rounded to the nearest whole number such that k (x) = 16 and interpret. (Source: National Center for Health Statistics) You Be the Teacher! Correct each student’s errors, if any. 93. Evaluate g (3) for g (x) = 7 - x2. Debbie’s work: g (x) = 7 - x2 g (3) = (7 - x2)(3) = 21 - 3x2 94. Evaluate g (-4) for g (x) = 2x2 + 5. Evan’s work: g (x) = 2x2 + 5 g (-4) = 2(-4)2 + 5 = 64 + 5 = 69 Calculate It! Use the TABLE feature in a calculator to evaluate each function at the specified value. Round each answer to two decimal places, when applicable. 95. f (x)=-4x 2 + 6x - 3, f (2.5) 96. f (x) = x 3 - 3x 2 + 5, f (-1.5) 97. g (x) = u7x + 5u , g (15) 98. g (x) = u19x - 21u, g (–19) Think About It! 99. Let f (x) = ux + 2u. a. Solve the equation f (x) = 4 using the methods from Section 2.6. b. Graph f (x) and draw a horizontal line through y = 4 on the same coordinate system. c. What are the points, if any, where the graph of f (x) and the horizontal line intersect? How do the points of intersection relate to the solutions of the equation? d. Solve f (x) < 4 using the methods from Section 2.7. e. On the graph from part (b), shade the portion of the x-axis that corresponds to the solution set of the inequality in part (d). f. How can the graph be used to solve the inequality?
hendricks_intermediate_algebra_1e_ch1_3
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