EXERCISE SET 3.3 Graphing Utility 1-14 Give a graph of the rational function and label the co- ordinates of the stationary points and inflection points. Show 17. Show that y = x + 3 is an oblique asymptote of the graph the horizontal and vertical asymptotes and label them with their of f(x) = x2/(x - 3). Sketch the graph of y = f(x) showing equations. Label point(s), if any, where the graph crosses a hor- this asymptotic behavior. izontal asymptote. Check your work with a graphing utility. 18. Show that y = 3 - x is a curvilinear asymptote of the 1. 2x - 6 graph of f(x) = (2 + 3x - x')/x. Sketch the graph of y = 8 2. 3. X f(x) showing this asymptotic behavior. 4 -x To board x2 - 4 10 6 x2 - 4 x201001 3835 4. x2 - 4 1 16 ch 5. 6. (x-1)2 19-24 Sketch a graph of the rational function and label the co- x2+ 4 x4+1 ordinates of the stationary points and inflection points. Show 7. : x +1 the horizontal, vertical, oblique, and curvilinear asymptotes and x3 - 8. 2 - 3x2+x3 label them with their equations. Label point(s), if any, where the add of ar gol nogo bruin seas graph crosses an asymptote. Check your work with a graphing 9. 3(x + 1)- utility. send aintoqutongs x2 r 10. (x- 1)2 19. x2 - 20. X - 2 (3x + 1)2 x +1 X X 11. (x - 1)2 12. 3 + (x - 1)4 21. ( x- 2)3 22. x - 1 13. * +x X r2 14. 1 - x2 1 - x 23. x - 4x - 8 x 24. 15-16 In each part, make a rough sketch of the graph using x + 2 x2 + 1 asymptotes and appropriate limits but no derivatives. Compare inite your graph to that generated with a graphing utility. 3x 2 - 8 x2 + 2x FOCUS ON CONCEPTS 15. (a) y = 2 4 (b) y= x2 - 1 25. In each part, match the function with graphs I-VI. 1/5