Characteristics of Exponential Functions

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Mathematics
•
9th Grade
•
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 horizontal asymptote of an exponential function?
Back
The horizontal asymptote of an exponential function is a horizontal line that the graph approaches as x approaches positive or negative infinity. For functions of the form f(x) = a * b^x, the horizontal asymptote is typically y = 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 the function approaches y = 0 as x approaches negative infinity.
4.
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 the graph crosses the y-axis, which occurs at (0, a).
5.
FLASHCARD QUESTION
Front
What does it mean for an exponential function to exhibit growth?
Back
An exponential function exhibits growth when the base 'b' is greater than 1, resulting in the function increasing rapidly as x increases.
6.
FLASHCARD QUESTION
Front
What does it mean for an exponential function to exhibit decay?
Back
An exponential function exhibits decay when the base 'b' is between 0 and 1, resulting in the function decreasing rapidly as x increases.
7.
FLASHCARD QUESTION
Front
What is the domain of an exponential function?
Back
The domain of an exponential function is all real numbers, represented as (-∞, ∞).
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