What is an exponential function?
Graphs of Exponential Functions Review

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•
Mathematics
•
9th - 10th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.
2.
FLASHCARD QUESTION
Front
What does the graph of an exponential function look like?
Back
The graph of an exponential function is a smooth curve that either increases or decreases rapidly, depending on whether the base 'b' is greater than 1 (increasing) or between 0 and 1 (decreasing).
3.
FLASHCARD QUESTION
Front
What is the base of an exponential function?
Back
The base of an exponential function is the constant 'b' in the function f(x) = a * b^x. It determines the rate of growth or decay.
4.
FLASHCARD QUESTION
Front
What happens to the graph of an exponential function as x approaches infinity?
Back
As x approaches infinity, the graph of an exponential function with a base greater than 1 will rise towards infinity, while a base between 0 and 1 will approach zero.
5.
FLASHCARD QUESTION
Front
What is the y-intercept of an exponential function?
Back
The y-intercept of an exponential function f(x) = a * b^x is the point where x = 0, which is f(0) = a.
6.
FLASHCARD QUESTION
Front
How do you find the horizontal asymptote of an exponential function?
Back
The horizontal asymptote of an exponential function is typically y = 0, which the graph approaches but never touches as x approaches negative infinity.
7.
FLASHCARD QUESTION
Front
What is the difference between exponential growth and exponential decay?
Back
Exponential growth occurs when the base 'b' is greater than 1, leading to an increase in value. Exponential decay occurs when the base 'b' is between 0 and 1, leading to a decrease in value.
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