# Determine whether each equation determines y to be a function of x

• Jul 19th 2011, 04:45 PM
Prosercunus
Determine whether each equation determines y to be a function of x
I am just completely stuck on these problems. I am sort of making headway, but I am still confused.

$y^2=x$

I know the fundamentals of domain, range, function... but I have no idea how to solve the equation to see if it is a function.
• Jul 19th 2011, 05:20 PM
pickslides
Re: Determine whether each equation determines y to be a function of x
Have a go at graphing $y= \pm\sqrt{x}$

What do you notice?
• Jul 20th 2011, 02:57 PM
HallsofIvy
Re: Determine whether each equation determines y to be a function of x
Best way to do any such problem is to start with the definition! The definition of "function" is: given a relation between x and y, y is a function of x if and only if for any value of x, there is, at most, only one corresponding value of y. Now look at x= 1. What values of y give $y^2= 1$?
• Jul 22nd 2011, 02:33 AM
Duke
Re: Determine whether each equation determines y to be a function of x
Quote:

Originally Posted by HallsofIvy
Best way to do any such problem is to start with the definition! The definition of "function" is: given a relation between x and y, y is a function of x if and only if for any value of x, there is, at most, only one corresponding value of y. Now look at x= 1. What values of y give $y^2= 1$?

It should be that for every x in the domain, there is exactly one y in the co-domain associated with it. Not 'at most...one value of y' .
• Jul 23rd 2011, 04:50 AM
HallsofIvy
Re: Determine whether each equation determines y to be a function of x
That is not a correction of what I said, just a restatement. If "x" is not in the domain, there is no corresponding "y" hence "at most, only one corresponding value of y."