# How do you find the domain and range of y=-3sin(1/2)x?

Jun 2, 2018

Domain: all reals x
Range: $- 3 \le y \le 3$

#### Explanation:

$y = - 3 \sin \left(\frac{x}{2}\right)$
The amplitude is 3
The period (T) = $\frac{2 \pi}{n} = \frac{2 \pi}{\frac{1}{2}} = 4 \pi$

Now you can graph the equation like below.

graph{-3sin(x/2) [-10, 10, -5, 5]}

You will notice then that:
Domain: all reals x
Range: $- 3 \le y \le 3$

For the range, a tip is that for the range of the sine or cosine function, the range is always between the positive and negative amplitude.