Download Chapter P Review

Hour: _____
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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?