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Q13.

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Precalculus Mathematics for Calculus

Found in: Page 341

Book edition 7th Edition

Author(s) James Stewart, Lothar Redlin, Saleem Watson

Pages 948 pages

ISBN 9781337067508

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Short Answer

Graphing Exponential Functions Graph the function, not by plotting points, but by starting from the graph of $y = e x$ in Figure 1. State the domain, range, and asymptote.
$f (x) = e^{x - 2}$

The graph is:

The domain is $(- \infty, \infty)$ .

The range is $(0, \infty)$ .

The horizontal asymptote is $y = 0$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given.

The given function is $f (x) = e^{x - 2}$ .

Step 2. To determine.

We have to graph the given function, not by plotting points, but by starting from the graph of $y = e^{x}$ in Figure 1. Then we have to state the domain, range, and asymptote.

Step 3. Calculation.

The parent function of $f (x) = e^{x - 2}$ is $y = g (x) = e^{x}$ .

So,

$f (x) = e^{x - 2} = g (x - 2)$

It means we will move $y = e^{x}$ by 2 units to the right to graph $f (x) = e^{x - 2}$ .

Therefore, the graph is:

The possible x-values are all real numbers. So, the domain is $(- \infty, \infty)$ .

The y-values are from 0 to $\infty$ . So, the range is $(0, \infty)$ .

From the graph the horizontal asymptote is $y = 0$ .

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