Characteristics of Exponential Functions

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What is an exponential function?

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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.

Front

What is the general shape of an exponential growth function?

Back

The graph of an exponential growth function rises rapidly as x increases, starting from a low value and approaching infinity.

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CCSS.HSF-IF.C.7E

Front

What is the general shape of an exponential decay function?

Back

The graph of an exponential decay function decreases rapidly as x increases, approaching zero but never touching the x-axis.

Tags

CCSS.HSF-IF.C.7E

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

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CCSS.HSF-IF.C.7D

Front

How do you find the horizontal asymptote of an exponential function?

Back

For exponential growth functions, the horizontal asymptote is typically y=0. For exponential decay functions, it is also y=0.

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CCSS.HSF-IF.C.7E

Front

What does it mean if a function has a horizontal asymptote at y=3?

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It means that as x approaches infinity or negative infinity, the value of the function approaches 3.

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CCSS.HSF-IF.C.7D

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What is the domain of an exponential function?

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The domain of an exponential function is all real numbers, represented as (-∞, ∞).

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What is the range of an exponential growth function?

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The range of an exponential growth function is (0, ∞), meaning it can take any positive value.

Tags

CCSS.HSF-IF.C.7E

Front

What is the range of an exponential decay function?

Back

The range of an exponential decay function is (0, L), where L is the horizontal asymptote.

Tags

CCSS.HSF-IF.C.7E

Front

What is the difference between exponential growth and decay?

Back

Exponential growth occurs when the function increases rapidly, while exponential decay occurs when the function decreases rapidly.

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CCSS.HSF-IF.C.8B