Answer
$f(x)=\left(\dfrac{1}{2}\right)^x$
Work Step by Step
Substituting $x=
-3
$ and $f(x)=
8
$ in the given function, $f(x)=a^x$, then the value of $a$ is
\begin{array}{l}\require{cancel}
8=a^{-3}
\\\\
8=\dfrac{1}{a^3}
\\\\
a^3=\dfrac{1}{8}
\\\\
a=\sqrt[3]{\dfrac{1}{8}}
\\\\
a=\dfrac{1}{2}
.\end{array}
Hence, the equation of the given graph is $
f(x)=\left(\dfrac{1}{2}\right)^x
.$
