Exponential function transformations

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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 does it mean for an exponential function to be increasing?

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An exponential function is increasing if its output values grow larger as the input values increase, typically when the base 'b' is greater than 1.

Tags

CCSS.HSF-IF.C.7E

Front

What is the effect of a vertical stretch on an exponential function?

Back

A vertical stretch occurs when the function is multiplied by a factor greater than 1, making the graph taller without changing its horizontal position.

Tags

CCSS.HSF-IF.C.7E

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, f(x) = a * b^(x - h) shifts the graph 'h' units to the right.

Tags

CCSS.HSF-IF.C.7E

Front

What is the x-intercept of an exponential function?

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An exponential function does not have an x-intercept because it never crosses the x-axis; it approaches zero but never reaches it.

Tags

CCSS.HSF-IF.C.7E

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What is the common ratio in an exponential function?

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The common ratio is the factor by which the function's output changes for each unit increase in the input. For f(x) = a * b^x, the common ratio is 'b'.

Tags

CCSS.HSF-IF.C.8B

Front

How does a vertical compression affect an exponential function?

Back

A vertical compression occurs when the function is multiplied by a factor between 0 and 1, making the graph shorter.

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CCSS.HSF.BF.B.3

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What does the term 'asymptote' refer to in the context of exponential functions?

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

Tags

CCSS.HSF-IF.C.7E

Front

What is the transformation of the function y = 4^x to y = 2(4)^(x-3) + 1?

Back

The transformation includes a vertical stretch by a factor of 2, a horizontal shift to the right by 3 units, and a vertical shift up by 1 unit.

Front

What is the base of the exponential function f(x) = 2(4)^x?

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The base of the exponential function f(x) = 2(4)^x is 4.

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CCSS.HSF-IF.C.8B