Chapter 1.5, Problem 18E

(a)

To determine

To find: The equation of the graph that is obtained from the graph of $y=e^x$ and is reflected about the line $y=4$.

Answer to Problem 18E

The equation of the graph is $y=e^{-x}+8$.

Explanation of Solution

Start with the equation $y=e^x$.

The reflection of the graph of $y=e^x$ about the x-axis is $y=e^{-x}$.

The graph $y=e^x$ has y-intercept at $y=1$.

So, its reflection will pass through $y=-1$.

To reflect the graph about the line $y=4$ add 8 to both sides so, the reflected graph will pass through $y=4$.

Thus, the equation of the resultant graph is $y=-e^x+8$.

(b)

To determine

To find: The equation of the graph that is obtained from the graph of $y=e^x$ and is reflected about the line $x=2$.

Answer to Problem 18E

The equation of the graph is $y=e^{-x+4}$.

Explanation of Solution

Start with the equation $y=e^x$.

The reflection of the graph of $y=e^x$ about y-axis is $y=e^{-x}$.

When the function $y=e^{-x}$ is drawn then the vertical asymptote is zero.

In order to set $x=2$ in the centre of the graph of these two functions, add 4 units from the origin of x-axis in the rightward direction.

Thus, the equation of the resultant graph is $y=e^{-x+4}$.