PrepLion

Unit 4 of 5

Unit 4: Functions & Modeling

Study guide for CLEP CLEP Precalculus — Unit 4: Functions & Modeling. Practice questions, key concepts, and exam tips.

146

Practice Questions

23

Flashcards

4

Key Topics

Key Concepts to Study

Polynomial, rational, and piecewise functions
Exponential growth and decay models
Logarithmic functions and equations
Function transformations and composition

Sample Practice Questions

Try these 5 questions from this unit. Sign up for full access to all 146.

Q1MEDIUM

A population of bacteria grows according to the function P(t) = 200(1.5)^t, where t is the number of hours. Which of the following statements is true about this function?

A) The population is always decreasing.
B) The population is always increasing, and its graph is concave down.
C) The population is always increasing, and its graph is concave up.
D) The population is constant.
E) The population is always increasing, and its graph is linear.
Show Answer

Answer: C — Since b > 1, the function demonstrates exponential growth, and its graph is always concave up.

Q2MEDIUM

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?

A) I(x) = 64 / $x^{2}$
B) I(x) = 16 / x
C) I(x) = $16x^{2}$
D) I(x) = 4 / $x^{2}$
E) I(x) = 64 / x
Show Answer

Answer: A — Since intensity is inversely proportional to the square of distance, the model is I(x) = k / $x^{2}$. Given I(2) = 16, we find k by 16 = k / $2^{2}$, so k = 64.

Q3MEDIUM

Find the range of f(x) = |x|

A) (-∞, 0)
B) (0, ∞)
C) [0, ∞)
D) (-∞, 0]
E) (-∞, ∞)
Show Answer

Answer: C — "[0, ∞)" is correct because absolute value is non-negative.

Q4MEDIUM

What can be determined about a rational function if the input values sufficiently close to c correspond to output values arbitrarily close to L?

A) The function has a vertical asymptote at x = c
B) The function has a hole at the point (c, L)
C) The function is not defined at x = c
D) The function has a horizontal asymptote at y = L
E) The function has a vertical asymptote at x = L
Show Answer

Answer: B — If input values close to c correspond to output values close to L, then the hole is at (c, L), indicating the function is not defined at x = c but approaches L.

Q5MEDIUM

What is the inverse of the function f(x) = 2x + 1?

A) f^(-1)(x) = (1/2)x - 1/2
B) f^(-1)(x) = (1/2)x + 1/2
C) f^(-1)(x) = 2x - 1
D) f^(-1)(x) = x/2 + 1
E) f^(-1)(x) = x/2 - 1
Show Answer

Answer: A — 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.

Ready to master Unit 4: Functions & Modeling?

Get unlimited practice questions, AI tutoring, flashcards, and a personalized study plan. Start free — no credit card required.

Study Tips for Unit 4: Functions & Modeling

  • 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

CLEP® is a trademark registered by the College Board, which is not affiliated with, and does not endorse, this product.