Question

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

Answer 1

Domain = `RR` (all real numbers)
Range = `{-3, oo}`

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 `RR`.

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:
`{-3, oo}`