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

Explanation:

Step1: Analyze graph - transformation rules

For the function $y = e^x$, multiplying by - 1 reflects it over the x - axis, getting $y=-e^x$. Then adding 4 shifts it up 4 units to get $y=-e^x + 4$.

Step2: Find the domain

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

Step3: Find the range

We know that $e^x>0$ for all real x. Then $-e^x<0$. Adding 4 to both sides gives $-e^x + 4<4$. So the range of the function $y=-e^x + 4$ is $(-\infty,4)$.

Answer:

Domain: $(-\infty,\infty)$ Range: $(-\infty,4)$