# What is the range of y = 2^x-1?

The range of the given function can be determined by comparing this with the graph of $y = {2}^{x}$ . Its range is (0,$\infty$).
The given function is a vertical shift down by 1. Hence its range would be (-1,$\infty$)
Alternatively, interchange x and y and find the domain of the new function. Accordingly, x=${2}^{y}$-1, that is ${2}^{y}$= x+1. Now take natural log on both sides, y=$\frac{1}{\ln} 2 \ln \left(x + 1\right)$
The domain of this function is all real values of x greater than -1, that is (-1,$\infty$)