AP PreCalculus Practice Quiz: Logarithmic Functions

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 11 questions to check your progress.

Question 1 of 11

What is the domain of a logarithmic function in its general form?

A)All real numbersB)All real numbers greater than zeroC)All real numbers except zeroD)All real numbers greater than or equal to zero

All Questions (11)

What is the domain of a logarithmic function in its general form?

A) All real numbers

B) All real numbers greater than zero

C) All real numbers except zero

D) All real numbers greater than or equal to zero

Correct Answer: B

The provided content explicitly states, 'The domain of a logarithmic function in general form is any real number greater than zero...'

Which of the following describes the range of a logarithmic function in its general form?

A) All real numbers

B) All positive real numbers

C) All real numbers from -1 to 1

D) Only non-negative real numbers

Correct Answer: A

According to the provided text, the range of a logarithmic function 'is all real numbers.'

A logarithmic function in its general form has a vertical asymptote at which value of x?

A) x = 1

B) x = -1

C) x = 0

D) It has no vertical asymptote

Correct Answer: C

The content specifies that 'logarithmic functions in general form are vertically asymptotic to x = 0.'

Which statement accurately describes the monotonic and concave nature of a logarithmic function's graph?

A) It can switch from increasing to decreasing.

B) It is always increasing or always decreasing.

C) Its concavity can change from up to down.

D) It is always concave up.

Correct Answer: B

The text states that 'Logarithmic functions are also always increasing or always decreasing, and their graphs are either always concave up or always concave down.' Option B correctly identifies the monotonic property.

What is the end behavior of a logarithmic function in its general form?

A) It is bounded by a horizontal asymptote.

B) It approaches a specific finite value.

C) It is unbounded.

D) It is periodic.

Correct Answer: C

The provided content clearly states that a logarithmic function has 'an end behavior that is unbounded.'

A function f is determined to be logarithmic. According to the definition provided, what relationship exists for the transformation g(x) = f(x) + k?

A) Input values are additive over equal-length output intervals.

B) Output values are proportional over equal-length input intervals.

C) Input values are proportional over equal-length output value intervals.

D) Output values are equal over proportional input value intervals.

Correct Answer: C

This question directly tests the specific definition provided in the text: 'If the input values... are proportional over equal-length output value intervals, then f is logarithmic.'

Which of the following is NOT a guaranteed characteristic of a logarithmic function in its general form?

A) The domain is (0, ∞).

B) The range is (-∞, ∞).

C) The graph is always concave down.

D) The graph has a vertical asymptote at x = 0.

Correct Answer: C

The content states that the graphs of logarithmic functions 'are either always concave up or always concave down.' It does not guarantee that a given function is always one or the other, just that it doesn't change concavity.

A function is described as having a domain of all real numbers greater than zero, a range of all real numbers, and an unbounded end behavior. Which type of function fits this description?

A) Exponential

B) Logarithmic

C) Quadratic

D) Linear

Correct Answer: B

This combination of characteristics—domain (x>0), range (all real numbers), and unbounded end behavior—is explicitly described in the provided content for logarithmic functions.

For a function f, it is observed that for any constant output interval C (i.e., f(x₂) - f(x₁) = C), the ratio of the corresponding inputs (x₂/x₁) is always the same. This property indicates that f is what type of function?

A) Linear

B) Exponential

C) Power

D) Logarithmic

Correct Answer: D

This is a direct application of the rule provided: 'equal-length output value intervals' (f(x₂) - f(x₁) = C) corresponds to 'proportional' input values (x₂/x₁ = constant). This defines a logarithmic function.

Which of the following sets of graphical features is possible for a single logarithmic function?

A) Always decreasing and changes concavity.

B) Always increasing and always concave up.

C) Increases on one interval and decreases on another.

D) Has both a vertical and a horizontal asymptote.

Correct Answer: B

The content states logarithmic functions are 'always increasing or always decreasing' and 'either always concave up or always concave down.' Therefore, a function that is always increasing and always concave up is a valid possibility. The other options contradict these rules.

Which statement best combines the key boundary and end behaviors of a general logarithmic function?

A) It is horizontally asymptotic to y = 0 and its end behavior is bounded.

B) It is vertically asymptotic to x = 0 and its end behavior is unbounded.

C) It has no asymptotes and its end behavior is unbounded.

D) It is vertically asymptotic to x = 0 and its end behavior is bounded.

Correct Answer: B

This answer correctly combines two distinct facts from the content: 'logarithmic functions in general form are vertically asymptotic to x = 0' and have 'an end behavior that is unbounded.'