Answer
$f(x)=2^{2x+1}$
Work Step by Step
Substituting values of $x$ in the given function, $
f(x)=2^{2x+1}
$, results to
\begin{array}{c|c|c}
\text{If }x=-1: & \text{If }x=0 & \text{If }x=1
\\\\
f(x)=y=2^{2x+1} & f(x)=y=2^{2x+1} & f(x)=y=2^{2x+1}
\\
y=2^{2(-1)+1} & y=2^{2(0)+1} & y=2^{2(1)+1}
\\
y=2^{-2+1} & y=2^{0+1} & y=2^{2+1}
\\
y=2^{-1} & y=2^{1} & y=2^{3}
\\
y=\dfrac{1}{2^1} & y=2 & y=8
\\
y=\dfrac{1}{2}
.\end{array}
Tabulating the results above results to the table below.
\begin{array}{c|c}
\hline
x & y
\\\hline
-1 & \dfrac{1}{2}
\\\hline
0 & 2
\\\hline
1 & 8
\end{array}
Connecting the points $
\left(-1,\dfrac{1}{2}\right),
\left(0,2\right),
\text{ and }
\left(1,8\right)
$ with a curve gives the graph of $
f(x)=2^{2x+1}
$.
