Answer
$f(x)=5^x$
Work Step by Step
Substituting $x=
-1
$ and $f(x)=
\dfrac{1}{5}
$ in the given function, $f(x)=a^x$, then the value of $a$ is
\begin{array}{l}\require{cancel}
\dfrac{1}{5}=a^{-1}
\\\\
\dfrac{1}{5}=\dfrac{1}{a}
\\\\
a=5
.\end{array}
Hence, the equation of the given graph is $
f(x)=5^x
.$
