Answer
$y=3^{x}-2$
Work Step by Step
This graph is a graph of $f(x)=b^{x}$, shifted down 2 units
(the asymptote moved from y=0 to y=$-2)$.
To find the original function,
raising the graph upward, we move the points
($0,-1)$ to (0,1)
(where we expect the graph of $f(x)=b^{x}$ to pass through).
$(1,1) \rightarrow (1,3)\qquad 3=3^{1}$
$(2,7) \rightarrow (2,9)\qquad 9=3^{2}$,
The original function was $f(x)=3^{x}$,
shifted down 2 units,
$y=f(x)-2=3^{x}-2$
$y=3^{x}-2$
