College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.1 - Page 452: 52


please see image below (f(x)=red curve, g(x)=blue curve), asymptote of $f:\quad\quad y=0$ asymptote of $g:\quad\quad y=$2

Work Step by Step

Graph $ f(x)=(\displaystyle \frac{1}{2})^{x}\qquad$ (red) by plotting the points from the table and connecting with a smooth curve. $g(x)=(\displaystyle \frac{1}{2})^{x-1}+2=f(x-1)+2$ so the graph of $g(x)$ (blue) is obtained by shifting the graph of f(x) right by 1 unit, $f(x-1)$ (green dashed). then, shifting up by 2 units, $f(x-1)+2$, (blue) . Reading the graph, asymptote of $f:\quad\quad y=0$ (yellow, dashed) asymptote of $g:\quad\quad y=$2 (black, dashed
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