AP PreCalculus Flashcards: Logarithmic Functions
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 11 cards to help you master important concepts.
What is the concavity of a logarithmic function's graph?
The graph of a logarithmic function is either always concave up or always concave down.
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What is the concavity of a logarithmic function's graph?
The graph of a logarithmic function is either always concave up or always concave down.
Identify two key characteristics that define the shape of a logarithmic function's graph.
Logarithmic functions are always increasing or decreasing, and their graphs are always concave up or concave down.
How can you test if a function `f` is logarithmic by analyzing its additive transformation `g(x) = f(x) + k`?
The function `f` is logarithmic if its input values are proportional over equal-length output value intervals for the function `g(x)`.
Summarize the relationship between the domain, range, and vertical asymptote of a general logarithmic function.
A general logarithmic function has a domain of x > 0 and a range of all real numbers, with a vertical asymptote at x = 0 that bounds its domain.
What is the domain of a logarithmic function in its general form?
The domain of a logarithmic function in general form is any real number greater than zero (x > 0).
What graphical feature results from the limited domain of a logarithmic function?
The limited domain (x > 0) of a logarithmic function in its general form results in a vertical asymptote at x = 0.
A function's graph has a vertical asymptote at x=0, a range of all real numbers, and is always increasing. What type of function could this be?
Based on these key characteristics, the function is likely a logarithmic function.
What is the range of a logarithmic function?
The range of a logarithmic function is all real numbers.
Describe the monotonic behavior of logarithmic functions.
Logarithmic functions are always monotonic, meaning they are either always increasing or always decreasing across their entire domain.
Describe the end behavior of a logarithmic function.
The end behavior of a logarithmic function is unbounded, meaning as x increases, the function's value continues to increase or decrease without limit.
What is the vertical asymptote for a logarithmic function in its general form?
Logarithmic functions in general form are vertically asymptotic to the line x = 0 (the y-axis).