Question

below is the graph of $y = e^x$. transform it to make the graph of $y = e^{-x} + 5$. give the range and domain of $y = e^{-x} + 5$ using interval notation.

Explanation:

Step1: Find domain of \(y=e^{-x}+5\)

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

Step2: Find range of \(y=e^{-x}+5\)

\(e^{-x} > 0\) for all \(x\), so \(e^{-x}+5 > 5\). Range: \((5, \infty)\).

Answer:

Domain: \((-\infty, \infty)\)
Range: \((5, \infty)\)