Answer
Refer to the graph below.
Work Step by Step
RECALL:
The graph of the function $y=c+a\cdot \cos{[b(x-d)]}$ is a sinusoidal curve that has:
period = $\frac{2\pi}{b}$
amplitude = $|a|$
phase shift = $|d|$ (to the left when $d\lt0$, to the right when $d\gt0$)
one period is in the interval $[0, 2\pi]$
vertical shift = $|c|$ (upward when $|c|\gt0$, downward when $c\lt0$)
Write the given function in the form $y=c+a\cdot\cos{[b(x-d)]}$ by factoring out $\pi$ within the cosine function:
$y=0+(-\frac{1}{2})\cdot \cos{[\pi(x-1)]}$
The given function has $a=-\frac{1}{2}, b=\pi,c=0$ and $d=1$
Thus, the graph of this function has:
period = $\frac{2\pi}{\pi}=2$
amplitude = $|-\frac{1}{2}| = \frac{1}{2}$
phase shift = $|1| = 1$ , to the right
vertical shift = 0 (none)
Since $a$ is negative, the graph also involves a reflection about the x-axis f the parent function.
One period of this function will be in the interval $[0-1, 2-1]=[-1, 1]$.
Divide this interval into four equal parts to get the key x-values $-1, -0.5, 0, 0.5, 1$.
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 the points from the table of values and connect them using a sinusoidal curve. (Refer to the graph in the answer part above.)
