Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.2 Exponential Functions - 4.2 Exercises: 63

Answer

$y=3^{x}-2$

Work Step by Step

This graph is a graph of $f(x)=b^{x}$, shifted down 2 units (the asymptote moved from y=0 to y=$-2)$. To find the original function, raising the graph upward, we move the points ($0,-1)$ to (0,1) (where we expect the graph of $f(x)=b^{x}$ to pass through). $(1,1) \rightarrow (1,3)\qquad 3=3^{1}$ $(2,7) \rightarrow (2,9)\qquad 9=3^{2}$, The original function was $f(x)=3^{x}$, shifted down 2 units, $y=f(x)-2=3^{x}-2$ $y=3^{x}-2$
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