Note that if the exponential function is in the form `f(x)= a ^x + c` , the horizontal asymptote is `y = c` .

**Hence, the horizontal asymptote of the function `y = e^x - 1` is `y=-1` .**

Note that if the exponential function is in the form `f(x)= a ^x + c` , the horizontal asymptote is `y = c` .

**Hence, the horizontal asymptote of the function `y = e^x - 1` is `y=-1` .**