the graph of f. en multiplicity, then the graph of f city, then the graph of f the x-axis. -hand and left-hand behavior + ? X- formation shown in the graph allows you arantee that f has a zero in the interval [x1, x]? ofeven or odd multiplicity? 10. f(x) x2 12. f(x) = 2x 14. f(x) 16. f(x) = 9. f(x) = -2x + 3 ns In ith its 11. f(x) =-2x2 5x 13. f(x) = + 3x2 15. f(x) = x4 +2x3 Library of Parent Functions In E sketch the graph of y x3 and the grap f. Describe the transformation from y to 12 17. f(x) = (x - 2)3 E8 19. f(x) = 18. f(x) = 20. f(x) = 22. f(x) - x3 + 1 21. f(x) -(x- 2) 11 8 nction J. . Can fbe a fourth-degree polynomial function? . Can the leading coefficient of f be negative? 7. The graph shows that f(x)< 0. What other information shown in the g to apply the Intermediate Value Theorem to guarantee that f has a zero 8. Is the repeated zero off in the interval [x, xof even or odd multiplic Procedures and Problem Solving 9. f(x 11. f(x 13. f(x 15. f( dentifying Graphs of Polynomial Functions In Exercises 9-16, match the polynomial function with its graph. [The graphs are labeled (a) through (h). (а) 4 (b) 12 -12 -4 5 sketch f.Des -2 -8 17. f (c) (d) 5 19. f 21. f # TA -6 -7 8 3 Com -2 -5 grap Yat (f) (e) 9 sam 4 righ gra beh ts -4 5 -7 8 23. -1 V. e -2 24 (g) 4 (h) 2 25. .8 26 -3 6 8 -5 4 27 -2 28 -4 LO LO LO

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Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.