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

1 Answer
Jun 14, 2018

Answer:

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}#.