PROBLEM 1 Indicate whether the two functions are equal. If the two functions are not equal, hen give an element of the domain on which the two functions have different values. S:Z-Z, where f(z) = r². 9:Z+Z, where g(z) = |rj*. S:ZxZ+Z, where f(r. y) = |r+ yl- 9:Z xZ+ Z. where g(x, y) = |r| + lal-

Given a function f(x) with the function values ƒ(−6) = −24, ƒ(−2) = −20, ƒ(−1) = 0, and ƒ(4) = 64, which value of x is a factor of the function? A. x = -6 4. 5. The function y = 4(−x + 9)¹(2x − 3)²(x + 6) changes signs at A. x = -9 B. x = 9 C. x = A. B. x = -2 C. x = 3 6. Which list best represents the values of x that make the following equation true: 3x³ + 6x² + 11x + 6 = 0 ? A. +1, +2, +3, +6 B. ±1,±2, ±3,±6,±½‚±z C. +1, +2, +², +², +³ D. 0, 11, 12, 13, +++ 3x-1 7. 6x4 - 2x³ - 21x² + 7x +8 is divided by 3x – 1 to give a quotient of 2x³ 7x and a remainder of 8. Which statement is true? 6x4-2x³-21x² +7x+8 = 2x³ - 7x + C. x = -1 8 3x-1 8. What is the solution to − (x − 3)(x + 8) < 0 ? - A. x € (-∞, -3) U (8,00) 3 2 B. x € (-∞, -8) U (3,00) D. x = 4 2 D. x = -6 C. x € (-∞, -8] U [3,00⁰) B. 6x4 - 2x³ - 21x² + 7x+8 = (3x − 1)(2x³ – 7x) - 8 D. All of these statements are true D. x € (-8,3)

Suppose that the functions p and q are defined as follows. p (x) = -3x q (x) = 2x+4 Find the following. (a • p)(s) = 0 (p• 9)(s) = 0

Sand is being dumped from a hopper railcar at a rate of 40 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other (both are growing larger as more sand is dumped). How fast is the base diameter increasing when the base is 18 feet long? Round your answer to three decimal places. ft/min