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Hour: _____ Name: ___________________________ Date: ____________________________ Pre-Calculus: Chapter P Practice Test 1. Solve. Express your solution in interval notation. 4x 1 0 a) 2 3 c) 17 x 2 16 x 4 b) 2 5 2x 3 d) x3 2 x 2 4 x 8 0 2. Rewrite the absolute value function f x x 4 as a piecewise-defined function. 3. Determine the equation of the line that passes through the points (a, 6) and (–2, b), where a and b are the x-coordinates of the points of intersection of y x3 5x 2 2 x 100 and y x3 2 x 2 4 x 460. Let a be the greater of the two x-coordinates. (Hint: Read the problem again.) 4. A company’s profits P (in thousands of dollars) are modeled by the equation P x 2 12 x 2, where x represents the number of thousands of units produced. a) How many units should the company produce to generate the maximum profit? b) What is that profit? c) How many units must be produced to ensure a profit of at least $25,000? 5. A farmer plans to use 180 feet of fencing to enclose a rectangular region, using part of a straight river bank instead of fencing on one side of the rectangle. Find the area of the region if the length of the side parallel to the river bank is: a) twice the length of the adjacent side. b) one-half the length of an adjacent side. c) the same as the length of an adjacent side. 6. I’d like to know the interval where the graph of y x 4 3 is above the line y 2 . What problem could I give you that would have this information as its solution but not mention graphs? Solve the problem as you stated it and verify your solution algebraically. 2 7. Consider the polynomial function f x 2 x3 10x2 48x . a) Solve the equation f x 0 . b) Explain how the process you used in part (a) to solve an equation differs from what you would need to do to solve the inequality f x 0 . c) Solve the inequality f x 0 . Express your solution in interval notation. d) What is another way I could have asked you to solve the inequality f x 0 without ever mentioning inequality?