Graphing Exponential Functions

Flashcard
•
Mathematics
•
9th - 12th 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 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 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 y = a * b^x, the horizontal asymptote is typically y = 0.
3.
FLASHCARD QUESTION
Front
What does the base of an exponential function determine?
Back
The base of an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.
4.
FLASHCARD QUESTION
Front
What is the domain of the function y = 2^x?
Back
The domain of the function y = 2^x is all real numbers, expressed as (-∞, ∞).
5.
FLASHCARD QUESTION
Front
What is the range of the function y = 2^x?
Back
The range of the function y = 2^x is all positive real numbers, expressed as (0, ∞).
6.
FLASHCARD QUESTION
Front
How does a vertical shift affect the graph of an exponential function?
Back
A vertical shift moves the graph up or down. For example, y = 2^x + 3 shifts the graph of y = 2^x up by 3 units.
7.
FLASHCARD QUESTION
Front
How does a horizontal shift affect the graph of an exponential function?
Back
A horizontal shift moves the graph left or right. For example, y = 2^(x - 1) shifts the graph of y = 2^x to the right by 1 unit.
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