The curve appears to be that of an exponential function. It appears to go through the points (1, 1) and (2, 4). That is, the y-value is multiplied by 4 when the x-value increases by 1. The function y = 4^x would go through the point (0, 1), so this graph appears to be shifted to the right one unit. We believe it is a graph of
... y = 4^(x-1)
The horizontal asymptote of an exponential function with no vertical shift is ...
... y = 0
