# How do you find the domain and range of y = x^2 - 3?

$x \in \mathbb{R} , y \ge - 3$

#### Explanation:

The domain is the list of valid $x$ values. Here, there are no values of $x$ that are disallowed (0 is ok, small positive and negative values are ok, big positive and negative values are ok). And so we can say that the domain is:

$x \in \mathbb{R}$

The range is the list of resulting values after we plug in $x$ values. See that the smallest value ${x}^{2}$ can be is 0 - it can't be negative. And so the smallest value ${x}^{2} - 3$ can be is $- 3$. This means the range is:

$y \ge - 3$

Here's the graph that will show this:

graph{x^2-3}