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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.

88

Practice Questions

25

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 88.

Q1MEDIUM

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 decreasing over the interval.
B) The function is increasing 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: B — 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

Graph of y = |x| + 2 is

A) U-shaped with vertex at (0, 0)
B) Linear with slope 1
C) U-shaped with vertex at (0, 2)
D) V-shaped with vertex at (0, 0)
E) V-shaped with vertex at (0, 2)
Show Answer

Answer: E — "V-shaped with vertex at (0, 2)" is correct because it's a V-shaped graph shifted 2 units up.

Q3MEDIUM

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.

Q4MEDIUM

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..

Q5MEDIUM

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

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

Answer: D — "(0, -4)" is correct because it's the minimum point of the parabola.

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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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