How do you decide whether the relation #x^2-3y =12# defines a function?

1 Answer
Nov 1, 2015

A function is when for every #x# there is a maximum of only one #y#

Explanation:

Let's rewrite the relation by adding #3y# to both sides and subtracting #12# (also on both sides) and then divide by #3#:

#x^2-3y=12->x^2-12=3y->y=1/3x^2-4#
graph{x^2/3-12 [-28.86, 28.87, -14.43, 14.43]}
This gives one #y#-value for every #x#, so this may be called #y(x)#, or #y# as a function of #x#.

Note :
You can not write #x(y)#, or #x# as a function of #y#, because for many #y#'s there are two possible #x#'s.