College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.1 - Exponential Functions - 4.1 Exercises: 22

Answer

$\color{blue}{f(x)=5^x}$.

Work Step by Step

The graph of the function $f(x)=a^x$ contains the point $(-1,\frac{1}{5})$. This means that when $x=-1$, $f(-1) = \frac{1}{5}$. Substitute $x$ and $y$ into $f(x) =a^x$ to obtain: $\begin{array}{ccc} \\&f(x) &= &a^x \\&f(-1) &= &a^{-1} \\&\dfrac{1}{5} &= &a^{-1}\end{array}$ Use the rule $a^{-m}=\dfrac{1}{a^m}$ to obtain: $\dfrac{1}{5} = \dfrac{1}{a}$ Cross-multiply to obtain: $1(a) = 1(5) \\a=5$ With $a=5$, the function whose graph is given is $\color{blue}{f(x)=5^x}$.
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