7-2 Properties of Exponential Functions

Objectives

To explore the properties of functions of the form y = a b x y equals , eh b to the x

To graph exponential functions that have base e

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You can apply the four types of transformations—stretches, compressions, reflections, and translations—to exponential functions.

Essential Understanding The factor a in y = a b x y equals eh , b to the x  can stretch or compress, and possibly reflect the graph of the parent function y = b x . y equals , b to the x , .

The graphs of y = 2 x y equals , 2 to the x  (in red) and y = 3 · 2 x y equals 3 middle dot , 2 to the x  (in blue) are shown. Each y-value of y = 3 · 2 x y equals 3 middle dot , 2 to the x  is 3 times the corresponding y-value of the parent function y = 2 x . y equals , 2 to the x , .

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y = 3 · 2 x y equals 3 middle dot , 2 to the x  stretches the graph of the parent function y = 2 x y equals , 2 to the x  by the factor 3.

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