Unit 4 of 5
Study guide for CLEP CLEP Precalculus — Unit 4: Functions & Modeling. Practice questions, key concepts, and exam tips.
122
Practice Questions
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Key Topics
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A population of bacteria grows according to the function P(t) = 200, where t is the number of hours. Which of the following statements is true about this function?
The population is always decreasing.
The population is always increasing, and its graph is concave down.
The population is always increasing, and its graph is concave up.
The population is constant.
The population is always increasing, and its graph is linear.
Answer: C — Since b > 1, the function demonstrates exponential growth, and its graph is always concave up.
A study found that the intensity of a certain type of sound wave is inversely proportional to the square of the distance from the source. If the intensity is 16 units at a distance of 2 meters, which rational function could model the intensity I(x) in terms of distance x?
I(x) = 64 / x
I(x) = 16 / x
I(x) =
I(x) = 4 /
I(x) = 64 /
Answer: E — The intensity of the sound wave is inversely proportional to the square of the distance, so the function must be of the form I(x) = k / $x^{2}$. Given that I(2) = 16, the constant k must be 64, since 64 / $2^{2}$ = 16.
What is the inverse of the function f(x) = 2x + 1?
(x) = x/2 - 1
(x) = (1/2)x + 1/2
(x) = 2x - 1
(x) = x/2 + 1
(x) = (1/2)x - 1/2
Answer: E — To find the inverse of f(x), swap x and y and solve for y: x = 2y + 1, x - 1 = 2y, (x - 1)/2 = y.
A company's profit function is given by P(x) = - 5x + 1, where x is the number of units sold. What is the average rate of change of the profit function on the interval [2, 5]?
-4
-3
-1
7
11
Answer: A — Calculate the average rate of change using (P(5) - P(2)) / (5 - 2) = (2*$5^{2}$ - 5*5 + 1 - (2*$2^{2}$ - 5*2 + 1)) / 3 = -4
A function f(x) has an average rate of change of 2 over the interval [0, 2] and an average rate of change of -3 over the interval [2, 4]. Which of the following statements is true about the function?
The function is increasing over the entire interval [0, 4].
The function is decreasing over the entire interval [0, 4].
The function is increasing over the interval [0, 2] and decreasing over the interval [2, 4].
The function is decreasing over the interval [0, 2] and increasing over the interval [2, 4].
The function is constant over the interval [0, 4].
Answer: C — Average rate of change is positive over [0, 2] and negative over [2, 4], indicating the function increases then decreases.
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