Answer
Refer to the graph below.
Work Step by Step
RECALL:
The graph of the function $y=a\cdot \sin{(bx)}$ is a sinusoidal curve that has:
period = $\frac{2\pi}{b}$
amplitude = $|a|$
one period is in the interval $[0, \frac{2\pi}{b}]$
The given function has $a=2$ and $b=\pi$.
Thus, the graph of this function has:
period = $\frac{2\pi}{\pi}=2$
amplitude = $|2| = 2$
One period of this function will be in the interval $[0, 2]$.
Divide this interval into four equal parts to get the key x-values $0, 0.5, 1, 1.5, 2$.
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.)
