Exercise 1.4.16

Question

Starting with the graph of $y=e^{x}$, find the equation of the graph that results from

\begin{enumerate}[label=(\alph*)]
\item reflecting about the line $y=4$.

\item  reflecting about the line $x=2$.

\end{enumerate}

Khagan Gulusoy · Accepted Answer

\begin{enumerate}[label=(\alph*)]
\item To find this equation, we first find the equation of the graph obtained by reflecting the graph of the initial equation about the $x$-axis. The graph we obtained crosses the paint $(\ln 4,-4)$. Thus, we shift it up by 8 units so that it crosses the point $(\ln 4,4)$ :

$$
y=-e^{x}+8.
$$

\item  To find this equation, we first find the equation of the graph obtained by effecting the graph of the initial equation about the $y$-axis. Then, we shift it to the right by 4 units and obtain the graph of the desired equation. Thus, the desired equation is:

$$
y=e^{4-x}.
$$
\end{enumerate}

Exercise 1.4.16

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Exercise 1.4.16

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