Answer
$ H(x)=-3^{-x}.$
Work Step by Step
We first find the graph of $ f(x)=3^{x}$ among the graphs given from 19 to 24.
The graph of $ f(x)=3^{x}$ is
- always above the x-axis, (graphs 20, 22, 24)
- from left to right, always rises and passes through (0,1) and (1,3)
The graph of $ f(x)=3^{x}$ is graph 22.
This graph (graph 19) is obtained from the graph of $ f(x)=3^{x}$ by
reflecting it about the ${\it x}- axis$: $ f(-x)$
and then reflecting $ f(-x)$ about the $ y $-axis: $-f(-x)=-3^{-x}$
$ H(x)=-3^{-x}.$
