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

Jun 14, 2018

Domain and range are both $\setminus m a t h \boldsymbol{R}$

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 $\setminus m a t h \boldsymbol{R}$ and range $\setminus m a t h \boldsymbol{R}$ as well.

The domain is $\setminus m a t h \boldsymbol{R}$ because a line is, in particular, a polynomial, and every polynomial can be computed for every $x$.

The range is $\setminus m a t h \boldsymbol{R}$ 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:

${\lim}_{x \setminus \to - \infty} f \left(x\right) = - \setminus \infty , \setminus q \quad {\lim}_{x \setminus \to \infty} f \left(x\right) = \setminus \infty$

or

${\lim}_{x \setminus \to - \infty} f \left(x\right) = \setminus \infty , \setminus q \quad {\lim}_{x \setminus \to \infty} f \left(x\right) = - \setminus \infty$

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 $\setminus m a t h \boldsymbol{R}$.