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K Math 155 Lab (3.5-3.8).pdf Q 324 CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS For the following exercises, find the slant asymptote. 41. f(x) = 4 x2 - 1 42. f (x) = 2x - x2+ 4 * +2 x2 + 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 MODELING USING VARIATION For the following exercises, find the unknown value. 49. y varies directly as the square of x. If when x = 3, 50. y varies inversely as the square root of x. If when y = 36, find y if x = 4. x = 25, y = 2, find y if x = 4. 51. y varies jointly as the cube of x and as z. If when 52. y varies jointly as x and the square of z and inversely x = 1 and z = 2, y = 6, find y if x = 2 and z = 3 as the cube of w. If when x = 3, z = 4, and w = 2, y = 48, find y if x = 4, z = 5, and w = 3. For the following exercises, solve the application problem. 53. The weight of an object above the surface of the 54. The volume V of an ideal gas varies directly with the earth varies inversely with the distance from the temperature T and inversely with the pressure P. center of the earth. If a person weighs 150 pounds A cylinder contains oxygen at a temperature of when he is on the surface of the earth (3,960 miles 310 degrees K and a pressure of 18 atmospheres in a from center), find the weight of the person if he is 20 volume of 120 liters. Find the pressure if the volume miles above the surface. is decreased to 100 liters and the temperature is increased to 320 degrees K.DIVIDING POLYNOMIALS For the following exercises, use long division to find the quotient and remainder. 25, X - 2x2 + 4x + 4 26. 3x# - 4x2 + 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 x + 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. 3x3 + 11x2 + 8x - 4= 0 33. 2x4 - 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) = - 3x2 - 27 40. f(x) = *+2 x2 + x - 2