The asymptote of the parent function 
, 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
will be shifted 4 units above as compared to the asymptote of 
.Therefore, the asymptote of is y=4
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