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Math Help - Determine whether each equation determines y to be a function of x

  1. #1
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    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.
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  2. #2
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    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?
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  3. #3
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    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 [itex]y^2= 1[/itex]?
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  4. #4
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    Re: Determine whether each equation determines y to be a function of x

    Quote Originally Posted by HallsofIvy View Post
    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 [itex]y^2= 1[/itex]?

    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' .
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  5. #5
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    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."
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