AP PreCalculus Flashcards: Exponential Functions
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 14 cards to help you master important concepts.
For the function f(x) = 5(0.8)^x, identify the initial value and the base.
The initial value 'a' is 5, and the base 'b' is 0.8.
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For the function f(x) = 5(0.8)^x, identify the initial value and the base.
The initial value 'a' is 5, and the base 'b' is 0.8.
A function f(x) is known to be exponential. What does this imply about the values of g(x) = f(x) + 10 over equal input intervals?
This implies that the output values of g(x) will be proportional over any equal-length input-value intervals.
Describe the monotonicity of an exponential function's graph.
The graph of an exponential function is either always increasing or always decreasing across its entire domain.
What are the restrictions on the base 'b' in an exponential function?
The base 'b' must be a positive number greater than zero and cannot be equal to one (b > 0, and b ≠ 1).
Identify the two main parameters in the general form of an exponential function.
The two main parameters are 'a', the initial value (a ≠ 0), and 'b', the base (b > 0, b ≠ 1).
In the function f(x) = ab^x, what does the variable 'a' represent?
The variable 'a' represents the initial value of the function, provided that 'a' is not equal to zero.
What is the end behavior of an exponential function as x approaches infinity if 0 < b < 1 and a > 0?
The output values will get arbitrarily close to zero.
List two key graphical characteristics of an exponential function.
An exponential function's graph is always increasing or decreasing, and it is always concave up or concave down.
What condition involving an additive transformation indicates that a function 'f' is exponential?
If the values of the additive transformation function g(x) = f(x) + k are proportional over equal-length input-value intervals, then the function f is exponential.
What is a key characteristic of the concavity of an exponential function's graph?
The graph of an exponential function is either always concave up or always concave down.
What is the domain of an exponential function?
The domain of an exponential function is all real numbers.
How do the output values of an exponential function behave as input values increase or decrease without bound?
As input values change without bound, the output values will either increase or decrease without bound, or they will get arbitrarily close to zero.
What is the general form of an exponential function?
The general form is f(x) = ab^x, where 'a' is the non-zero initial value and 'b' is the base, which must be positive and not equal to 1.
What is the end behavior of an exponential function as x approaches infinity if the base b > 1 and a > 0?
The output values will increase without bound, approaching positive infinity.