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

1 Answer
John D.
Aug 22, 2015

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}

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