Concept explainers
In Exercises 1–6, use the given rational function to find the indicated function values. If a Function value does not exist, so state.
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Intermediate Algebra for College Students (7th Edition)
- 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 – 5arrow_forwardExercises 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)arrow_forwardIn Exercises 29–30, find f(-x) – f(x) for the given function f. Then simplify the expression. 29. f(x) = x + x - 5 30. f(x) = x² – 3x + 7arrow_forward
- The 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)arrow_forwardExercises 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) - 2arrow_forwardExercises 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 + 3arrow_forward
- 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 – x²arrow_forwardLet f(x) = 5x + 5arrow_forwardExercises 1-6: Identify f as being linear, quadratic, or neither. If f is quadratic, identify the leading coefficient a and evaluate f(-2). 1. f(x) = 1 – 2x + 3x? 2. f(x) = -5x + 11 3. f(x) = - x 4. f(x) = (x² + 1)² 5. f(x) = } - * 6. f(x) = }r?arrow_forward
- Let f(x) = 4x + 1, g(x) = x² - x - 6 and h(x) x +8 . Find and simplify the indicated composite function. X-8 (h ० n(x)arrow_forwardWrite an equation of the form f(x) = a* +b from the given graph. Then compute f(2). 8- 7- 6- f(x) |(1,6.3) 5- 4- 3- 10.2) X -4 -3 -2 -11- 3 4 f(x) = (Use integers or decimals for any numbers in the expression.)arrow_forwardLet f(x) = 2x + 1, g(x) = x² - x - 3 and h(x) x + 3 Find and simplify the indicated composite function. %3D X - 3 (h o g)(x) Find the domain. (Enter your answer using interval notation.)arrow_forward
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education