Question

1. starting with the graph of $y = e^x$, find the equation of the graph that results from

(a) reflecting about the line $y = 4$.
(b) reflecting about the line $x = 2$.

Explanation:

Step1: Reflect $y=e^x$ over $y=4$

Let $(x,y)$ be on new graph. Its reflection over $y=4$ is $(x, 8-y)$, which lies on $y=e^x$. Substitute: $8-y = e^x$, rearrange to $y = 8 - e^x$.

Step2: Reflect $y=e^x$ over $x=2$

Let $(x,y)$ be on new graph. Its reflection over $x=2$ is $(4-x, y)$, which lies on $y=e^x$. Substitute: $y = e^{4-x}$.

Answer:

(a) $y = 8 - e^x$
(b) $y = e^{4-x}$