below is the graph of y = e^x. transform it to make the graph of y=-e^(x - 4). give the range and domain of…

Answer:

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

Explanation:

Step1: Analyze function transformations

The original function is $y = e^{x}$. The new - function $y=-e^{x - 4}$ has two transformations. First, a reflection about the $x$ - axis due to the negative sign in front of $e^{x}$, and second, a horizontal shift of 4 units to the right.

Step2: Find the domain

For the exponential function $y = -e^{x - 4}$, there are no restrictions on the value of $x$. We can substitute any real - number for $x$ into the function. So, the domain is all real numbers, which in interval notation is $(-\infty,\infty)$.

Step3: Find the range

The range of the function $y = e^{x}$ is $(0,\infty)$. After reflecting it about the $x$ - axis (multiplying by - 1), the range of $y=-e^{x}$ is $(-\infty,0)$. The horizontal shift of 4 units to the right does not affect the range. So, the range of $y=-e^{x - 4}$ is $(-\infty,0)$.