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

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What is the horizontal asymptote of an exponential function?

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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 f(x) = a * b^x + k, the horizontal asymptote is y = k.

Tags

CCSS.HSF-IF.C.7E

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What is the y-intercept of an exponential function?

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The y-intercept of an exponential function is the point where the graph crosses the y-axis, which occurs at (0, a) for the function f(x) = a * b^x.

Tags

CCSS.HSF-IF.C.7E

Front

What is the range of an exponential function?

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The range of an exponential function f(x) = a * b^x is all real numbers greater than 0 if a > 0, or all real numbers less than 0 if a < 0.

Tags

CCSS.HSF-IF.C.7E

Front

What does it mean if an exponential function is increasing?

Back

An exponential function is increasing (exponential growth) if the base 'b' is greater than 1, meaning the function's value increases as x increases.

Tags

CCSS.HSF-IF.C.8B

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What does it mean if an exponential function is decreasing?

Back

An exponential function is decreasing (exponential decay) if the base 'b' is between 0 and 1, meaning the function's value decreases as x increases.

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What is the general shape of the graph of an exponential growth function?

Back

The graph of an exponential growth function rises steeply to the right and approaches the horizontal asymptote to the left.

Tags

CCSS.HSF-IF.C.7E

Front

What is the general shape of the graph of an exponential decay function?

Back

The graph of an exponential decay function falls steeply to the right and approaches the horizontal asymptote to the left.

Tags

CCSS.HSF-IF.C.7E

Front

How do you determine if a function is exponential growth or decay from its equation?

Back

If the base 'b' in the function f(x) = a * b^x is greater than 1, it is exponential growth. If 'b' is between 0 and 1, it is exponential decay.

Tags

CCSS.HSF-IF.C.8B

Front

What is the significance of the base 'b' in an exponential function?

Back

The base 'b' determines the rate of growth or decay of the function. A larger base results in faster growth, while a base less than 1 results in decay.

Tags

CCSS.HSF-IF.C.8B