# Chapter 4, Exponential and Logarithmic Functions - Section 4.1 - Exponential Functions - 4.1 Exercises - Page 372: 21

$\color{blue}{f(x)=3^x}$

#### 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 $\color{blue}{f(x)=3^x}$.

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