Answer
$y=-(2^{x+2}-3 )$
Work Step by Step
The graph of the original function $f(x)=b^{x}$ passes through (0,1),
and has the x-axis as the asymptote.
The shape of this graph suggests there was a reflection about the x-axis.
We reflect this graph, and get new points:
(0,1), (-1,-1) and (-2,-2),
and the asymptote is y=-3.
To move the asymptote back to y=0, we raise this graph by three units.
New points:
(0,4), (-1,2) and (-2,1).
Since f(x) passes through (0,1), we need to move (-2,1) to the right by 2 units.New points:
(2,4), (1,2) and (0,1)
The original function was $f(x)=2^{x},$
which was
shifted left 2 units $(2^{x+2}),$
lowered by 3, ($2^{x+2}-3$ ),
and reflected about the x-axis, resulting in
$y=-(2^{x+2}-3 )$
