Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 11 - Systems of Equations and Inequalities - Chapter Review - Cumulative Review - Page 797: 9


See graph Domain: $(-\infty,\infty)$ Range: $(1,\infty)$ Horizontal asymptote: $y=1$

Work Step by Step

We are given the function: $f(x)=3^{x-2}+1$ We start graphing the parent function $a(x)=3^x$. We horizontally shift $a(x)$ 2 units to the right to get $b(x)=3^{x-2}$. Finally vertically shift $b(x)$ one unit upward to get $f(x)=3^{x-2}+1$. Determine the domain: $(-\infty,\infty)$ Determine the range: $3^{x-2}>0$ $3^{x-2}+1>0+1$ $f(x)>1$ $(1,\infty)$ As $x\rightarrow -\infty,f(x)\rightarrow 1$ Therefore there is a horizontal asymptote: $y=1$
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