371 3.4 Polynomial Functions: Graphs, Applications, and Models 3.4 Exercises CONCEPT PREVIEW Comprehensive graphs of four polynomial functions are shown in A–D. They represent the graphs of functions defined by these four equations, but not necessarily in the order listed. y = x3 - 3x2 - 6x + 8 y = x4 + 7x3 - 5x2 - 75x y = -x3 + 9x2 - 27x + 17 y = -x5 + 36x3 - 22x2 - 147x - 90 Apply the concepts of this section to work each problem. C. x y 25 5 –25 0 D. x y 0 100 3 –6 5 –1 –100 –1300 Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. See Example 1. 9. ƒ1x2 = 2x4 10. ƒ1x2 = 1 4 x6 11. ƒ1x2 = - 2 3 x5 12. ƒ1x2 = - 5 4 x5 13. ƒ1x2 = 1 2 x3 + 1 14. ƒ1x2 = -x4 + 2 15. ƒ1x2 = -1x + 123 + 1 16. ƒ1x2 = 1x + 223 - 1 A. x y 5 0 4 –2 B. x y 25 –100 0 3 –5 1. Which one of the graphs is that of y = x3 - 3x2 - 6x + 8? 2. Which one of the graphs is that of y = x4 + 7x3 - 5x2 - 75x? 3. How many real zeros does the function graphed in C have? 4. Which one of C and D is the graph of y = -x3 + 9x2 - 27x + 17? 5. Which of the graphs cannot be that of a cubic polynomial function? 6. Which one of the graphs is that of a function whose range is not 1-∞, ∞2? 7. The function ƒ1x2 = x4 + 7x3 - 5x2 - 75x has the graph shown in B. Use the graph to factor the polynomial. 8. The function ƒ1x2 = -x5 + 36x3 - 22x2 - 147x - 90 has the graph shown in D. Use the graph to factor the polynomial.
RkJQdWJsaXNoZXIy NjM5ODQ=