Answer
Refer to the graph below.
Work Step by Step
RECALL:
(1) The function $y=a\cdot \sec{x}$ has a period of $2\pi$.
(2) Consecutive asymptotes of the secant function are $x=\frac{\pi}{2}$ and $x=\frac{3\pi}{2}$
One period of the given function is in the interval $[0, 2\pi]$.
The guide function for secant is $y=\frac{1}{2}\cos{x}$.
Divide this interval onto four equal parts to get the key x-values $0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi$.
To graph the given function, perform the following steps:
(1) Create a table of values for the guide function $y=\frac{1}{2}\cos{x}$ using the key x-values listed above. (Refer to the table below.)
(2) Plot the points from the table of values and connect them using a dashed curve (as the curve will only serve as a guide).
(3) Graph the consecutive vertical asymptotes listed above.
(4) Sketch the graph of $y=\frac{1}{2}\sec{x}$ by drawing
(i) a U-shaped curve below the x-axis and between the consecutive vertical asymptotes.
(ii) a half U-shaped curve from the point $(0, 0.5)$ to the asymptote $x=\frac{\pi}{2}$.
(iii) a half U-shaped curve from the asymptote $x=\frac{3\pi}{2}$ to the point $(2\pi, 0.5)$ .
(Refer to the graph in the answer part above.)
