Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.2 - The Natural Exponential Function - 4.2 Exercises - Page 341: 8

Answer

$\text{Domain: } (-\infty, \infty) \\\text{Range: } (-3,\infty) \\\text{Horizontal Asymptote: } y=-3 $

Work Step by Step

The black graph is the graph given in Figure 1, $y= e^x $. The red graph is the graph of the given function, $ h(x)=e^{-x}-3 $. It is the result of reflecting the the black graph about the $y-$axis and shifting by $3$ units down. The red graph has the following characteristics: \begin{array}{l}\require{cancel} \text{Domain: } (-\infty, \infty) \\\text{Range: } (-3,\infty) \\\text{Horizontal Asymptote: } y=-3 .\end{array}
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