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…

Explanation:

Step1: Identify graph - transformations

For $y = e^{x}$ to $y=-e^{x + 4}$, first reflect $y = e^{x}$ about the $x$ - axis (due to the negative sign in front of $e^{x}$) and then shift it 4 units to the left (because of $x+4$).

Step2: Find the domain

The exponential - type function $y=-e^{x + 4}$ is defined for all real values of $x$. So, the domain is all real numbers. In interval notation, the domain is $(-\infty,\infty)$.

Step3: Find the range

We know that the range of $y = e^{x}$ is $(0,\infty)$. After reflecting about the $x$ - axis, the range of $y=-e^{x}$ is $(-\infty,0)$. Shifting the graph 4 units to the left does not change the range. So, the range of $y=-e^{x + 4}$ is $(-\infty,0)$.

Answer:

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