let f(x) = 3^x

this graph has f(x) > 0

then 3^(x+2) -1

is a transformation on f(x)

so:

f(x+2) - 1

this is a vertical translation of -1 and a horizontal translation of left 2 units

we care only about the vertical translation

now we have f(x) > -1

so the horizontal asymptote is y = -1

since the curve approaches -1 when x is large negative