What is the equation for the asymptote of the function f(x)=2^x?

The functin f(x) = 2^x is an exponential function.

It does not have vertical asymptotes because the function is defined for all the real  values.

To find the horizontal asymptotes calculate the limits when the function grows positively and negatively.

The limif of 2^x when x goes to + infinity is infinity so there is not asymptote to this side.

The limit of 2^x when x goes to - infinity is 0, so y = 0 is an asymptote.

the equation for the asymptote is y = 0.