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

Aug 22, 2015

Domain = $\mathbb{R}$ (all real numbers)
Range = $\left\{- 3 , \infty\right\}$

#### Explanation:

This is a simple 2nd degree equation with no denominator or anything, so you will always be able to choose ANY number for x, and get a "y" answer. So, the domain (all possible x-values) is equal to all real numbers. The common symbol for this is $\mathbb{R}$.

However, the highest degree term in this equation is an ${x}^{2}$ term, so this equation's graph will be a parabola. There isn't just a regular ${x}^{1}$ term, so this parabola will not be shifted left or right any; it's line of symmetry is exactly on the y-axis.

This means that whatever the y-intercept is is the lowest point of the parabola. Luckily, that point is simply the $- 3$ that the equation gives us (on the y-axis, x = 0, so ${x}^{2} - 3$ is just $0 - 3$ or $- 3$).

So, the range of this equation is from $- 3$ all the way up to positive infinity. The correct way to show this is like this:
$\left\{- 3 , \infty\right\}$