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: 29

Answer

please see graph (blue curve), asymptote of $h$:$\quad\quad y=-1$ domain of $h=(-\infty,\infty)$ range of $h=(-1,\infty)$

Work Step by Step

Graph $ f(x)=2^{x}\qquad$ (red, dashed) by plotting the points from the table and connecting with a smooth curve. $h(x)=2^{x+1}-1=f(x+1)-1$ so the graph of $h(x)$ (blue) is obtained by shifting the graph of f(x) (red) left by one unit, $[2^{x+1}]$, (dashed green) and then down by one unit, $[2^{x+1}-1]$, (blue) Reading the graph, asymptote of $h$:$\quad\quad y=-1$ domain of $h=(-\infty,\infty)$ range of $h=(-1,\infty)$
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