Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.1 - Exponential Functions - Exercise Set - Page 449: 46


See graph; asymptote $y=2$ Domain: $(-\infty,\infty)$ and range: $(2,\infty)$

Work Step by Step

Step 1. Start from the original function $f(x)=e^x$ shown as the green curve in the figure. Step 2. To obtain the new curve of $h(x)=e^{x/2}+2$, stretch the original horizontally by a factor of 2, then shift the result vertically 2 units up to get the red curve as shown. Step 3. We can identify the new asymptote as $y=2$ Step 4. We can determine the domain as $(-\infty,\infty)$ and range as $(2,\infty)$
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