The asymptote of the parent function [tex] 3^{x} [/tex], like any other similar exponential function is y = 0.
But in this case the parent function is transformed. It is shifted vertically upward by 4 units. When an exponential function is shifted vertically up or down its asymptote is also shifted by same number of units.
Hence, the asymptote of [tex]f(x)= 3^{x}+4 [/tex] will be shifted 4 units above as compared to the asymptote of [tex]f(x)= 3^{x} [/tex] .Therefore, the asymptote of [tex]f(x)= 3^{x}+4 [/tex] is y=4
