Answer
$h(x)=-4^{-x}$
Work Step by Step
The graph of $f(x)=b^{x}$, when $b\gt 1$, has the following characteristics:
- it is above the x-axis at all times, always rising,
- on the far left, it nears, but never touches the x-axis,
- it rises to cross the y-axis at the point (0,1)
- it rises to pass through the point (1,b),
- and keeps rising...
The graph (4) corresponds to this description, and it is the graph of $f(x)=4^{x}.$
We obtain this graph (graph 2) from graph 4 by
reflecting it across the y-axis, (generating the graph of $f(-x)$ )
and then reflecting it across the x-axis, (generating the graph of $-f(-x)$ )
$-f(-x)$ = $h(x)=-4^{-x}$
