Question

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

Answer 1

Domain: all real numbers.
Range: `[-16,-4]`.

Explanation:

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

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