# How do you find the domain and range of y = x + 3?

$x \in \mathbb{R} , y \in \mathbb{R}$

#### Explanation:

The Domain is the list of all allowable $x$ values. Sometimes, equations have $x$ values that can't be used. Here are a couple of examples:

$\frac{1}{x}$ - since we can't divide by 0, $x \ne 0$

$\sqrt{x}$ - since we can't get real number solutions to a negative number under the square root sign, we tend to say that we can't have negative values, and so $x \ge 0$

In our case, there are no values of $x$ that are disallowed. And so any real value can be an $x$ value, or

$x \in \mathbb{R}$ - which says $x$ can be any real value

The Range is the list of all values arising from the domain (which in this case are the $y$ values).

In our case, when $x$ is large, so will $y$. When $x$ is a large negative, so will $y$. In fact, we can arrive at any value $y$ by picking the correct value of $x$. And so we can say:

$y \in \mathbb{R}$

And we can see this in the graph:

graph{x+3}