Question

below is the graph of $y = e^x$. transform it to make the graph of $y = -e^{x + 2}$. give the range and domain of $y = -e^{x + 2}$ using interval notation.

Explanation:

Step1: Find domain of \(y=-e^{x+2}\)

Exponential functions accept all real \(x\). Domain: \((-\infty, \infty)\).

Step2: Find range of \(y=-e^{x+2}\)

\(e^{x+2} > 0\) for all \(x\). Multiply by -1: \(-e^{x+2} < 0\). Range: \((-\infty, 0)\).

Answer:

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