Answer
Graph:
.
Work Step by Step
Graph $f_{1}(x)=4^{x}$ first. Points:
$\left\{\begin{array}{l}
(-1,1/4)\\
(0,1),\\
(1/2,2)\\
(1,4)
\end{array}\right.$
We obtain the graph of $f(x)$ by vertically stretching $f_{1}(x)$ by the factor $2$. Points:
$\left\{\begin{array}{l}
(-1,1/2)\\
(0,2),\\
(1/2,4)\\
(1,8)
\end{array}\right.$
We obtain the graph of $g(x)$ by reflecting $f(x)$ about the y-axis. Points:
$\left\{\begin{array}{l}
(+1,1/2)\\
(0,2),\\
(-1/2,4)\\
(-1,8)
\end{array}\right.$
