# What is the domain and range of y=2x+3?

Aug 6, 2015

Domain is $x \epsilon \mathbb{R}$
Range is $y \epsilon \mathbb{R}$

#### Explanation:

There are no limitations placed on possible values of $x$ [the Domain] (for example, no value of $x$ would cause an attempt to divide by zero)
so $x$ can take on any value. (for the purposes of this question I've assumed that you are working with Real numbers, $\mathbb{R}$, but $x$ could in fact be any complex , $\mathbb{C}$, value.

We can see that any value within $\mathbb{R}$ (or $\mathbb{C}$) could be generated for $y$ (the Range) by noting that the inverse of the function:
$x = \frac{y - 3}{2}$ places no limitations on the value of $y$