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

1 Answer
Aug 22, 2015

Answer:

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}#