Question

What is the domain and range of `y=-3x-3`?

Answer 1

Domain and range are both `\mathbb{R}`

Explanation:

Note that your equation describes a line, since it is a polynomial of first degree. As a general result, every non-constant line has domain `\mathbb{R}` and range `\mathbb{R}` as well.

The domain is `\mathbb{R}` because a line is, in particular, a polynomial, and every polynomial can be computed for every `x`.

The range is `\mathbb{R}` because a non-constant line is either always growing or decreasing at a constant rate.

This means that, for every line, you always have one of this two situations:

`lim_{x \to -infty} f(x) = -\infty,\qquadlim_{x \to infty} f(x) = \infty`

or

`lim_{x \to -infty} f(x) = \infty,\qquadlim_{x \to infty} f(x) = -\infty`

and since every polynomial is continuous, it spans all the possible values from its minimum to its maximum. In other words, every line spans all the possible values from `-infty` to `infty`, which means all the real number, thus the range is `\mathbb{R}`.