Answer
$r(x)$
Work Step by Step
The graph of $f(x)=4^{x}$ passes through (0,1) and (1,4)
($4^{0}=1$ and $4^{1}=4).$
This graph is not $f(x)=4^{x}$ (but can be obtained from it).
This graph passes through (0,$-1$) and ($-1,-4$),
which are obtained from (0,1) and (1,4) by:
reflecting about the y-axis $\qquad $
$\quad\rightarrow(0,1)$ and ($-1$,4),$\quad f(x)\rightarrow f(-x)$,
then, reflecting about the x axis,
$\quad \rightarrow(0,-1)$ and ($-1,-$4),$\quad f(-x)\rightarrow-f(-x)$,
and then shifting up by three units,
$\quad \rightarrow(0,2)$ and ($-1,-$1),$\quad -f(-x)\rightarrow-f(-x)+3$,
So this function is
$-f(-x)+3=-4^{-x}+3=r(x)$
