College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.2 - The Natural Exponential Function - 4.2 Exercises - Page 377: 8

Answer

Domain: $(-\infty,\infty)$ Range: $(-3,\infty)$ Asymptote: $y=-3$

Work Step by Step

We are given the function: $$h(x)=e^{-x}-3.$$ Consider the function $f(x)=e^x$ as the parent function. First we obtain the graph of $g(x)=e^{-x}$ by reflecting the graph of $f$ across the $y$-axis. Then we vertically shift the graph of $g$ by $3$ units down to obtain the graph of $h(x)=e^{-x}-3$ (see the graph). From the graph we determine the following elements of function $g$: - the domain: $$\text{domain}=(-\infty,\infty)$$ - the range: $$\text{range}=(-3,\infty)$$ - the horizontal asymptote: $$y=-3.$$
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