It's what you call as a "line".
g(x) has the smallest possible y-value of -3. This is because f(x)=3^x-3 is an exponetial graph that has been shifted down three units. It has an asymptote at y=-3. This means that it comes to -3 but isn't going to contact it.
Y - 3 = -2(x+5)
y - 3 = -2x - 10
+3. +3
y = -2x - 7