SECTION 4.6 The Graph of a Rational Function 255 Figure 56 π = + Y x x 0.10 20 1 3 0 0 60 10 Substituting πr 500 2 for h, we find that the cost C, in cents, as a function of the radius r is π π π π π ( ) = + ⋅ = + = + C r r r r r r r r 0.10 0.04 500 0.10 20 0.10 20 2 2 2 3 (b) See Figure 56 for the graph of ( ) = C C r using a TI-84 Plus CE. (c) Using the MINIMUM command, the cost is least for a radius of about 3.17 centimeters. (d) The least cost is ( ) ≈ C 3.17 9.47¢. Now Work PROBLEM 63 ‘Are You Prepared?’ The answer is given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 4.6 Assess Your Understanding 1. Find the intercepts of the graph of the equation = − − y x x 1 4 . 2 2 (pp. 20–21) Concepts and Vocabulary 2. True or False The graph of every rational function has at least one asymptote. 3. Multiple Choice Which type of asymptote will never intersect the graph of a rational function? (a) horizontal (b) oblique (c) vertical (d) all of these 4. True or False The graph of a rational function sometimes has a hole. 5. ( ) ( ) = − − R x x x x 2 2 2 (a) Find the domain of R. (b) Find the x -intercepts of R. 6. Multiple Choice Identify the y -intercept of the graph of ( ) ( ) ( )( ) = − + + R x x x x 6 1 1 2 . (a) −3 (b) −2 (c) −1 (d) 1 Skill Building In Problems 7–50, follow Steps 1 through 7 on page 249 to graph each function. 7. ( ) ( ) = + + R x x x x 1 4 8. ( ) ( )( ) = − + R x x x x 1 2 9. ( ) = + + R x x x 3 3 2 4 10. ( ) = + − R x x x 2 4 1 11. ( ) = − R x x 3 4 2 12. ( ) = − − R x x x 6 6 2 13. ( ) = + + − P x x x x 1 1 4 2 2 14. ( ) = − − Q x x x 1 4 4 2 15. ( ) = − − H x x x 1 9 3 2 16. ( ) = + + G x x x x 1 2 3 2 17. ( ) = + − R x x x x 6 2 2 18. ( ) = + − − R x x x x 12 4 2 2 19. ( ) = − G x x x 4 2 20. ( ) = − G x x x 3 1 2 21. ( ) ( ) ( ) = − − R x x x 3 1 4 2 22. ( ) ( ) ( ) = − + − R x x x 4 1 9 2 23. ( ) = − − H x x x 1 16 2 4 24. ( ) = + − H x x x 4 1 2 4 25. ( ) = − − + F x x x x 3 4 2 2 26. ( ) = + + − F x x x x 3 2 1 2 27. ( ) = + − − R x x x x 12 4 2 28. ( ) = − − + R x x x x 12 5 2 29. ( ) = + − + F x x x x 12 2 2 30. ( ) = − − + G x x x x 12 1 2 31. ( ) ( ) ( ) = − + R x x x x 1 3 2 3 32. ( ) ( )( )( ) ( ) = − + − − R x x x x x x 1 2 3 4 2 33. ( ) = + − − − R x x x x x 12 6 2 2 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure
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