Answer
Refer to the graph below.
Work Step by Step
RECALL:
The function $y=a \cdot \cos{[b(x-d)]}$
(1) has a period of $\dfrac{2\pi}{|b|}$;
(2) has an amplitude of $|a|$; and
(3) involves a phase shift of $|d|$ of the parent function $y=\cos{x}$ (to the left when $d\lt0$, to the right when $d\gt0$)
The given function has $a=1, b=1,$ and $d=\frac{\pi}{4}$.
Thus, the given function has:
period = $\frac{2\pi}{1}=2\pi$
amplitude = $|1|=1$
phase shift = $\frac{\pi}{4}$ to the right
One period of the parent function $y=\cos{x}$ is in the interval $[0, 2\pi]$
The given function has a phase shift of $\frac{\pi}{4}$ to the right therefore one period would be in the interval $[\frac{\pi}{4}, \frac{9\pi}{4}]$.
Divide this interval into four equal parts to obtain the key x-values $\frac{\pi}{4}, \frac{3\pi}{4} \frac{5\pi}{2}\frac{7\pi}{4}, \frac{9\pi}{4}$.
To graph the given function, perform the following steps:
(1) Create a table of values using the key x-values listed above. (Refer to the table below.)
(2) Plot each point from the table of values then connect them using a sinusoidal curve. (Refer to the graph in the answer part above.)
