32. Use a graphing utility to find the equation of the line of best fit. Write the equation of the line rounded to two decimal places, if necessary.

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1 Pre-Calculus A Final Review Part 2 Calculator Name 31. The price p and the quantity x sold of a certain product obey the demand equation: p = x + 80 where r = xp. What is the revenue to the nearest dollar when 200 units are sold? Round to the nearest integer, if necessary. 32. Use a graphing utility to find the equation of the line of best fit. Write the equation of the line rounded to two decimal places, if necessary. x y State the vertex and axis of symmetry 34. State the domain and the range of the for the graph of the f(x) = x 2 16x + 5 f(x) = x 2 + 6x The manufacturer of a CD player has found that the revenue R (in dollars) is R(p) = -5p p, when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest whole dollar?

2 36. The profit that the vendor makes per day by selling x pretzels is given by the function p(x) = x x 200. State the number of pretzels that must be sold to maximize profit. 37. A projectile is thrown upward so that its distance above the ground after t seconds is h = -12t t. After how many seconds does it reach its maximum height? 38. State the polynomial function, in general form, whose zeros and degree are given: zeros: -2, -5, 2; degree For the polynomial, list each real zero and its multiplicity. State whether the graph crosses or touches the x-axis at each x-intercept. f(x) = x2 (x 2 5)(x 6)

3 40. State the x- and y-intercepts of the 41. State the x- and y-intercepts of the f(x) = -x 2 5x 4 f(x) = -x 3 (x 4)(x 2 + 5) 42. Use the remainder theorem to find the remainder when f(x) is divided by x c. State the remainder. f(x) = x 4 + 8x x 2 ; x Use the Rational Zero Theorem to find all the real zeros of the polynomial Use the zeros to factor f over the real numbers. State the real zeros and the factored form of the polynomial f(x) = 2x 3 11x 2 + 7x + 20

4 44. State the real solutions of the equation. 4x 3 23x x + 8 = You have 724 feet of fencing to enclose a rectangular region. State the width of the rectangle that maximizes the enclosed area. 46. State the quadratic function, in general form, given the following: Vertex: (-2, -1) Y-int: (0, 5)

5 47. Find k such that f(x) = x 4 + kx has the factor of x + 2. State the value of k. 48. State a polynomial f(x), in general form, with real coefficients having the given degree and zeros. Degree: 3; zeros: -4 and 3 2i 49. Use the given zero to find the remaining zeros of the State the remaining zeros. f(x) = x 4 9x 2 10 zero: i

6 50. Use the given zero to find the remaining zeros of the f(x) = 5x 4 51x x 2 297x + 52 zero: 3 + 2i 51. State all zeros of the function, and write the polynomial as a product of linear factors. f(x) = x 3 + 2x 2 3x 10

7 52. State the domain of the rational 53. State the vertical asymptote(s) of the rational f(x) = f(x) = ( ) 54. State the equation of the horizontal 55. State the equation of the oblique asymptote, if any, of the asymptote, if any, of the f(x) = f(x) = 56. Evaluate the expression using the values given in the table. X f(x) X g(x) State the value of (f g)(3) 57. For the given functions f and g, state the requested composite function value. f(x) = 4x + 2 g(x) = 2x Find (g f)(2)

8 58. For the given functions f and g, state the requested composite function as a polynomial. f(x) = x g(x) = x Find (f g)(x) 59. Use the graph of the given one-to-one function to draw the graph of the inverse 60. The function f is one-to-one. State its inverse. f(x) = 5x 3