Exponential Functions

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•
Mathematics
•
9th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is an asymptote in the context of exponential functions?
Back
An asymptote is a line that a graph approaches but never touches. For exponential functions, horizontal asymptotes often represent the value that the function approaches as x approaches infinity or negative infinity.
2.
FLASHCARD QUESTION
Front
What does the 'a' represent in the exponential function y = a(b^x)?
Back
'a' represents the y-intercept of the function, which is the value of y when x = 0.
3.
FLASHCARD QUESTION
Front
What is the general form of an increasing exponential function?
Back
An increasing exponential function can be expressed in the form y = a(b^x) where a > 0 and b > 1.
4.
FLASHCARD QUESTION
Front
What is the domain of an exponential function?
Back
The domain of an exponential function is all real numbers, expressed as (-∞, ∞).
5.
FLASHCARD QUESTION
Front
What is the range of an exponential function?
Back
The range of an exponential function is all positive real numbers, expressed as (0, ∞).
6.
FLASHCARD QUESTION
Front
How do you determine the y-intercept of an exponential function?
Back
The y-intercept can be found by evaluating the function at x = 0, which gives the value of 'a' in the function y = a(b^x).
7.
FLASHCARD QUESTION
Front
What is the difference between exponential growth and exponential decay?
Back
Exponential growth occurs when the base 'b' in the function y = a(b^x) is greater than 1, while exponential decay occurs when 'b' is between 0 and 1.
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