Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 4 - Section 4.1 - Exponential Functions - 4.1 Exercises - Page 337: 38

Answer

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

Work Step by Step

The black graph is the graph given in Figure 2, $y= 10^x $. The red graph is the graph of the given function, $ f(x)=3-10^{x-1} $. It is the result of shifting the black graph by $1$ unit to the right, reflecting about the $x-$axis, and shifting $3$ units up. The red graph has the following characteristics: \begin{array}{l}\require{cancel} \text{Domain: } (-\infty, \infty) \\\text{Range: } (-\infty,3) \\\text{Horizontal Asymptote: } y=3 .\end{array}
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