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Chapter 5: Q. 60 (page 284)

Begin with the graph of y=exand use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

fx=7-3e2x

Short Answer

Expert verified

The graph of the function is given below,

Domain: All real numbers.

Range:-鈭�,7ory|y<7.

Horizontal asymptote:y=7

Step by step solution

01

Step 1. Given information.

Consider the given function,

fx=7-3e2x

First, plot the graph of y=ex. Replace xwith 2x. Multiply by -1 and reflect about y-axis. Add 7and shift up by 7units,

02

Step 2. Determine the characteristics of the function.

Consider the given function,

fx=7-3e2x

From the graph, the domain of the function is the set of all real numbers.

As we can see thatx鈫�-鈭�,fx鈫�7.

Thus the range is -鈭�,7or in the interval y|y<7.

Horizontal asymptote isy=7.

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