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Unit 3 of 5

Unit 3: Functions and Their Graphs

Study guide for CLEP CLEP College Algebra — Unit 3: Functions and Their Graphs. Practice questions, key concepts, and exam tips.

71

Practice Questions

57

Flashcards

10

Key Topics

Key Concepts to Study

domain and range
function notation
transformations
inverse functions
graphing
piecewise functions
scenario-to-graph reasoning (real-world piecewise modeling)
graph interpretation from verbal description
step functions
evaluating piecewise functions

Sample Practice Questions

Try these 5 questions from this unit. Sign up for full access to all 71.

Q1HARD

A company's profit from selling x units of a product is given by the function P(x) = $2x^{2}$ + 5x - 100. What is the behavior of the function over the interval where x > 5?

A) The function is increasing over the interval.
B) The function is decreasing over the interval.
C) The function is constant over the interval.
D) The function is undefined over the interval.
E) The function is increasing then decreasing over the interval
Show Answer

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.

Q2MEDIUM

Find the equation of the axis of symmetry for the parabola f(x) = $x^{2}$ - 4x + 3.

A) x = 1
B) x = 2
C) x = 0
D) x = -2
E) x = -1
Show Answer

Answer: B — x = 2 is correct because x = -b / 2a = 4 / 2 = 2.

Q3EASY

For the function f(x) = 1 / (x - 2), what is the vertical asymptote?

A) x = 1
B) x = -2
C) x = -1
D) x = 0
E) x = 2
Show Answer

Answer: E — x = 2 is correct because the function is undefined when x - 2 = 0..

Q4EASY

Given f(x) = $x^{2}$ - 4, what is the vertex of the parabola?

A) (0, 4)
B) (0, -4)
C) (2, 0)
D) (0, 0)
E) (-2, 0)
Show Answer

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.

Q5EASY

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?

A) The profit decreases by a constant amount each year.
B) The profit increases by a proportionally constant amount each year.
C) The profit increases by a constant amount each year.
D) The profit increases by a constant percentage each year
E) The profit remains the same each year.
Show Answer

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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Study Tips for Unit 3: Functions and Their Graphs

  • Focus on understanding concepts, not memorizing facts — CLEP tests application
  • Practice with timed questions to build exam-day speed
  • Review explanations for wrong answers — they reveal common misconceptions
  • Use flashcards for key terms, practice questions for deeper understanding

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