# How do you find the domain & range for -3 cos x?

Feb 24, 2017

Domain: $\left(- \infty , \infty\right)$
Range: $\left[- 3 , 3\right]$

#### Explanation:

The domain is all the valid input values. Since cosine is a periodic function (it repeats), the domain is all real values: $\left(- \infty , \infty\right) .$

The $3$ says that the cosine function has an amplitude of $3$. The amplitude is the half-height of the wave so that means the range of the function is $\left[- 3 , 3\right]$.

The negative sign in front of the amplitude says that the wave is reversed. This means instead of $\left(0 , 3\right)$, for the peak, it has $\left(0 , - 3\right)$ as the trough if the wave.

Graph of $f \left(x\right) = - 3 \cos \left(x\right)$:
graph{-3cos(x) [-10, 10, -5, 5]}