Identifying Characteristics Exponential Graphs

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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 the base (a positive real number), and 'x' is the exponent.

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What is the characteristic of exponential growth?

Back

In exponential growth, the function increases rapidly as 'x' increases, and the base 'b' is greater than 1.

Tags

CCSS.HSF-IF.C.8B

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What is the characteristic of exponential decay?

Back

In exponential decay, the function decreases rapidly as 'x' increases, and the base 'b' is between 0 and 1.

Tags

CCSS.HSF-IF.C.8B

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What does the term 'asymptote' refer to in exponential graphs?

Back

An asymptote is a line that a graph approaches but never touches. For exponential functions, the horizontal asymptote is often y=0.

Tags

CCSS.HSF-IF.C.7E

Front

How can you identify an exponential growth function from a graph?

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An exponential growth function will show a curve that rises steeply to the right, indicating rapid increase.

Tags

CCSS.HSF-IF.C.7E

Front

How can you identify an exponential decay function from a graph?

Back

An exponential decay function will show a curve that falls steeply to the right, indicating rapid decrease.

Tags

CCSS.HSF-IF.C.7E

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What is the value of f(1) in the exponential function f(x) = 3^x?

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f(1) = 3.

Tags

CCSS.HSF-IF.C.8B

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What is the value of f(0) in any exponential function?

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f(0) = a, where 'a' is the initial value of the function.

Tags

CCSS.HSF.LE.B.5

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What happens to the value of an exponential decay function as x approaches infinity?

Back

As x approaches infinity, the value of an exponential decay function approaches 0.

Tags

CCSS.HSF-IF.C.7E

Front

What happens to the value of an exponential growth function as x approaches infinity?

Back

As x approaches infinity, the value of an exponential growth function approaches infinity.

Tags

CCSS.HSF-IF.C.7E