What is an exponential function?
Exponential Functions

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Mathematics
•
11th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
An exponential function is a mathematical function of the form y = 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 is the general form of an exponential growth function?
Back
The general form of an exponential growth function is y = a * b^x, where b > 1.
3.
FLASHCARD QUESTION
Front
What is the general form of an exponential decay function?
Back
The general form of an exponential decay function is y = a * b^x, where 0 < b < 1.
4.
FLASHCARD QUESTION
Front
How do you determine if an exponential function represents growth or decay?
Back
If the base 'b' of the exponential function is greater than 1, it represents growth. If 'b' is between 0 and 1, it represents decay.
5.
FLASHCARD QUESTION
Front
What is the range of the function y = 2^(x+1) - 3?
Back
The range of the function y = 2^(x+1) - 3 is (-3, ∞).
6.
FLASHCARD QUESTION
Front
What does the term 'asymptote' refer to in the context of exponential functions?
Back
An asymptote is a line that a graph approaches but never touches. For exponential functions, the horizontal asymptote is typically the line y = k, where k is a constant.
7.
FLASHCARD QUESTION
Front
What is the effect of changing the base 'b' in an exponential function?
Back
Changing the base 'b' affects the rate of growth or decay. A larger base results in faster growth, while a smaller base (greater than 0 but less than 1) results in faster decay.
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