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- In Exercises 20–22, find the domain of each function. 20. f(x) = 7x - 3 1 21. g(x) x + 8 3x 22. f(x) = x + x - 5The function f(x) = 0.4x2 – 36x + 1000 models the number of accidents, f(x), per 50 million miles driven as a function of a driver's age, x, in years, for drivers from ages 16 through 74, inclusive. The graph of f is shown. Use the equation for f to solve Exercises 45–48. 1000 flx) = 0.4x2 – 36x + 1000 16 45 74 Age of Driver 45. Find and interpret f(20). Identify this information as a point on the graph of f. 46. Find and interpret f(50). Identify this information as a point on the graph of f. 47. For what value of x does the graph reach its lowest point? Use the equation for f to find the minimum value of y. Describe the practical significance of this minimum value. 48. Use the graph to identify two different ages for which drivers have the same number of accidents. Use the equation for f to find the number of accidents for drivers at each of these ages. Number of Accidents (per 50 million miles)Exercises 103–110: Let the domain of f(x) be [-1,2] and the range be [0, 3 ]. Find the domain and range of the following. 103. f(x – 2) 104. 5/(x + 1) 105. -/(x) 106. f(x – 3) + 1 107. f(2x) 108. 2f(x – 1) 109. f(-x) 110. -2/(-x)
- For Exercises 57–62, find and simplify f(x + h). (See Example 6) 59. f(x) = 7 – 3x 62. f(x) = x – 4x + 2 57. f(x) = -4x – 5x + 2 58. f(x) = -2x² + 6x – 3 60. f(x) = 11 – 5x² 61. f(x) = x' + 2x – 5In Exercises 1–6, find the domain and range of each function.1. ƒ(x) = 1 + x2 2. ƒ(x) = 1 - 2x3. F(x) = sqrt(5x + 10) 4. g(x) = sqrt(x2 - 3x)5. ƒ(t) = 4/3 - t6. G(t) = 2/t2 - 16For Exercises 103–104, given y = f(x), remainder a. Divide the numerator by the denominator to write f(x) in the form f(x) = quotient + divisor b. Use transformations of y 1 to graph the function. 2x + 7 5х + 11 103. f(x) 104. f(x) x + 3 x + 2
- Exercises 125-130: Evaluate the expression for the given function f. 125. f(a + 2) for f(x) = 3 – 4x² 126. f(a – 3) for S(x) = x² + 2x 127. f(a + h) for f(x) = x² – x + 5 128. f(a – h) for {(x) = 1 – 4x – x² 129. f(a + h) – f(a) for f(x) = 2x² + 3 130. f(a + h) – f(a) for f(x) = x – x²Exercises 111-114: Determine the domain and range of function f. Use interval notation. 111. f(x) = =(x + 1)² – 5 112. f(x) = 2(x – 5)² + 10 113. f(x) = V-x – 4 – 2 114. f(x) = -Vx – 1 + 3Example. Differentiate f(r) (4r- 5x +4(7-). n
- Exercises 3 and 4: Write f(x) in the general form f(x) = ax? + bx + c, and identify the leading coefficient. 3. f(x) = -2(x – 5)² + 1 4. f(x) = }(x + 1) - 2In Exercises15–36, find the points of inflection and discuss theconcavity of the graph of the function. f(x)=\frac{6-x}{\sqrt{x}}Evaluate the function h(x) = x* + 7x +1 at the given values of the independent variable and simplify. a. h(1) b. h(-1) c. h(- x) d. h(3a)