Unit 3 of 5
Study guide for CLEP CLEP College Algebra — Unit 3: Functions and Their Graphs. Practice questions, key concepts, and exam tips.
70
Practice Questions
57
Flashcards
10
Key Topics
Try these 5 questions from this unit. Sign up for full access to all 70.
A company's profit from selling x units of a product is given by the function P(x) = + 5x - 100. What is the behavior of the function over the interval where x > 5?
The function is increasing over the interval.
The function is decreasing over the interval.
The function is constant over the interval.
The function is undefined over the interval.
The function is increasing then decreasing over the interval
Answer: A — Since the coefficient of $x^{2}$ is positive, the parabola opens upward. For x > 5, as x increases, P(x) also increases, indicating the function is increasing.
Find the equation of the axis of symmetry for the parabola f(x) = - 4x + 3.
x = 1
x = 2
x = 0
x = -2
x = -1
Answer: B — x = 2 is correct because x = -b / 2a = 4 / 2 = 2.
For the function f(x) = 1 / (x - 2), what is the vertical asymptote?
x = 1
x = -2
x = -1
x = 0
x = 2
Answer: E — x = 2 is correct because the function is undefined when x - 2 = 0..
Given f(x) = - 4, what is the vertex of the parabola?
(0, 4)
(0, -4)
(2, 0)
(0, 0)
(-2, 0)
Answer: B — The vertex of a parabola in the form f(x) = ax^2 + bx + c is found at the point (h, k) where h = -b/2a and k = f(h), and since f(x) = x^2 - 4 has a = 1 and b = 0, the vertex is at (0, -4) because the parabola opens upward with its minimum value at x = 0.
A company's profit is modeled by the function f(x) = 2000 + 500x, where x is the number of years since the company's founding. Which of the following best describes the growth of the company's profit over equal-length time intervals?
The profit decreases by a constant amount each year.
The profit increases by a proportionally constant amount each year.
The profit increases by a constant amount each year.
The profit increases by a constant percentage each year
The profit remains the same each year.
Answer: C — The function f(x) = 2000 + 500x is a linear function, which means the profit increases by a constant amount (500) each year.
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