below is the graph of y = e^x. transform it to make the graph of y = e^(-x)-1. give the range and domain of…

Explanation:

Step1: Analyze graph transformation

The transformation from $y = e^{x}$ to $y=e^{-x}-1$ involves two steps. First, a reflection about the y - axis (due to the negative exponent) and then a vertical shift down by 1 unit.

Step2: Find the domain

For the function $y = e^{-x}-1$, the exponential function $e^{-x}=\frac{1}{e^{x}}$ is defined for all real - valued $x$. So the domain of $y = e^{-x}-1$ is all real numbers. In interval notation, the domain is $(-\infty,\infty)$.

Step3: Find the range

We know that the range of the exponential function $y = e^{-x}$ is $(0,\infty)$ since $e^{-x}=\frac{1}{e^{x}}>0$ for all $x\in R$. After a vertical shift down by 1 unit, the range of $y = e^{-x}-1$ is obtained by subtracting 1 from each value in the range of $y = e^{-x}$. So the range is $(-1,\infty)$.

Answer:

Domain: $(-\infty,\infty)$ Range: $(-1,\infty)$