please do problems 25, 26, 27, 28, 37, 38, 41, 46, and 47 and please show work

For the following exercises, based on the given graph, determine the zeros of the function and note multiplicity. 22. 23. 20 x 6 8 10 -12+ -16 -20 24. Use the Intermediate Value Theorem to show that at least one zero lies between 2 and 3 for the function f(x) = x - 5x+1 DIVIDING POLYNOMIALS For the following exercises, use long division to find the quotient and remainder. 25. X - 2x2 + 4x + 4 26. 3x* - 4x7 + 4x + 8 x - 2 x+1 For the following exercises, use synthetic division to find the quotient. If the divisor is a factor, then write the factored form. 27. X - 2x2 + 5x - 1 28. * + 4x + 10 *+3 x - 3 29. 2x + 6x2 - 11x - 12 30. 3x* + 3x3 + 2x + 2 x +4 x+1 ZEROS OF POLYNOMIAL FUNCTIONS For the following exercises, use the Rational Zero Theorem to help you solve the polynomial equation. 31. 2x3 - 3x2 - 18x - 8 = 0 32. 3x' + 11x' + 8x - 4 = 0 33. 2x" - 17x3 + 46x2 - 43x + 12 = 0 34. 4x* + 8x3 + 19x2 + 32x + 12 = 0 For the following exercises, use Descartes' Rule of Signs to find the possible number of positive and negative solutions. 35. x3 - 3x2 - 2x + 4 = 0 36. 2x4 - x3 + 4x2 - 5x + 1=0 RATIONAL FUNCTIONS For the following rational functions, find the intercepts and the vertical and horizontal asymptotes, and then use them to sketch a graph. 37. f(x) = *+2 x - 5 38. f(x) = *+1 x2 - 4 39. f (x) = - 3x - 27 x+x-2 40. f(x) = *+2 x2 - 9 324 CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS For the following exercises, find the slant asymptote. 41. f ( x ) = x - 1 42. f (x) = 2x' - x2+4 x + 2 x +1 INVERSES AND RADICAL FUNCTIONS For the following exercises, find the inverse of the function with the domain given. 43. f ( x) = (x - 2)2, x2 2 44. f(x) = (x+ 4)2 - 3, x2-4 45. f(x) = x +6x - 2, x2 -3 46. f(x) = 2x3 - 3 47. f(x) = V4x + 5 - 3 48. f(x) = x - 3 2x + 1