
Characteristics of Exponential Functions
Flashcard
•
Mathematics
•
9th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is an exponential function?
Back
An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.
2.
FLASHCARD QUESTION
Front
What is the x-intercept of a function?
Back
The x-intercept of a function is the point where the graph of the function crosses the x-axis, meaning f(x) = 0.
3.
FLASHCARD QUESTION
Front
What is the range of an exponential function?
Back
The range of an exponential function f(x) = a * b^x (where a > 0) is (0, ∞) if a is positive, and (-∞, 0) if a is negative.
4.
FLASHCARD QUESTION
Front
What does it mean for a function to approach a limit as x approaches negative infinity?
Back
As x approaches negative infinity, the function approaches a specific value, which can indicate horizontal asymptotic behavior.
5.
FLASHCARD QUESTION
Front
What is an asymptote?
Back
An asymptote is a line that a graph approaches but never touches. It can be horizontal, vertical, or oblique.
6.
FLASHCARD QUESTION
Front
How does the base of an exponential function affect its graph?
Back
The base (b) determines the growth rate: if b > 1, the function grows; if 0 < b < 1, the function decays.
7.
FLASHCARD QUESTION
Front
What is the vertical shift in an exponential function?
Back
A vertical shift occurs when a constant is added or subtracted from the function, affecting its position on the y-axis.
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