Answer
$\color{blue}{f(x)=3^x}$
Work Step by Step
The graph of the function $f(x)=a^x$ contains the point $(2, 9)$.
This means that when x=2, $f(2) = 9$.
Substitute $x$ and $y$ into $f(x) =a^x$ to obtain:
$\begin{array}{ccc}
\\&f(x) &= &a^x
\\&f(2) &= &a^2
\\&9 &= &a^2
\\&3^2 &= &a^2
\end{array}$
Using the rule "$a^mb^m \longrightarrow a = b$" gives:
$\begin{array}{ccc}&3 &= &a\end{array}$
With $a=3$, the function whose graph is given is $\color{blue}{f(x)=3^x}$.