# How do you find the domain and range of -3 cos x?

Dec 30, 2015

Domain = $\mathbb{R}$.
Rangge = $\left[- 3 , 3\right]$

#### Explanation:

Any general cosine graph of the form $y = A \sin B x$ has amplitude of $A$ (maximum vertical displacement from the rest position), and period $T = \frac{2 \pi}{B}$ representing the amount of units on the x-axis for 1 complete cycle of the graph to take place.

So in this particular case, $A = - 3 \mathmr{and} T = 2 \pi$.

So the domain being all possible x-values allowed is all real numbers $\mathbb{R}$, and the range being all possible y-values allowed is all y-values between $- 3 \mathmr{and} 3$, including the endpoints, ie the closed interval $\left[- 3 , 3\right]$.