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

1 Answer
KillerBunny
Jun 14, 2018

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}.

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