# What is the domain and range of K(t) = 6cos (90t) - 10?

Jun 6, 2016

Domain: all real numbers.
Range: $\left[- 16 , - 4\right]$.

#### Explanation:

The domain of a function $\cos \left(x\right)$ is all real numbers. Therefore, the domain of function $K \left(t\right) = 6 \cos \left(90 t\right) - 10$ is a set of all real numbers.

The range of function $\cos \left(x\right)$ is $\left[- 1 , 1\right]$.
Therefore, the range of $\cos \left(90 t\right)$ is the same $\left[- 1 , 1\right]$.
Multiplication of this by $6$ transforms the range to $\left[- 6 , 6\right]$.
Subtraction of $10$ from $6 \cos \left(90 t\right)$ shifts the range down by $10$, so it becomes $\left[- 16 , - 4\right]$.