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

Feb 27, 2016

$\mathrm{do} m f = \mathbb{R}$
$r a n f = \mathbb{R}$

#### Explanation:

$f \left(x\right) = x + 3$

Domain

Is there any value of $x$ that will make $f \left(x\right)$ undefined?

The answer to this is no, so the domain is the set of all real numbers $\mathbb{R}$.

$\mathrm{do} m f = \mathbb{R}$

Range

You will notice that the graph of $x + 3$ is just a line, meaning it will intersect all values of $y$ (since it increases and decreases without limit).

Therefore, the range is also the set of all real numbers $\mathbb{R}$.

$r a n f = \mathbb{R}$

Just keep this in mind. When you're given a linear function, its domain and range are both the set of all real numbers (unless the problem tells you it isn't).