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…

Answer:

Range: $(-\infty,0)$ Domain: $(-\infty,\infty)$

Explanation:

Step1: Analyze graph - transformations

For $y = e^{x}$ to $y=-e^{x - 1}$, first reflect $y = e^{x}$ about the $x$ - axis (due to the negative sign) and then shift it 1 unit to the right (because of $x-1$).

Step2: Find the domain

The exponential function $y = -e^{x - 1}$ is defined for all real values of $x$. So the domain is all real numbers, written as $(-\infty,\infty)$ in interval notation.

Step3: Find the range

The exponential function $e^{x-1}>0$ for all real $x$. When we multiply by - 1, we get $-e^{x - 1}<0$. So the range is all real numbers less than 0, written as $(-\infty,0)$ in interval notation.