# Math Help ## Recommended Posts  Hey, I was wondering if I could get some help with the following problem:

Give an example of an equation that does not define y as a function of x but does define x as a function of y.

Much appreciated!

##### Share on other sites  x=3y^2

##### Share on other sites Yeah, instead of having y = ax^2 + bx + x, just replace the y's with x's.

##### Share on other sites  as mentioned, y^2 = x is a great example.

why? let's use the inverse: y = x^2. think about the definition of a function, but we also know some properties, e.g. for every x, there is at most one y. in other words, it passes the vertical line test. as you move a vertical line, it intersects the function at only one point. this function fails the horizontal line test. as you move a horizontal line, it intersects the function twice. 2 different x values give the same y value.

what you're asking for is a type of expression that fails the vertical line test. the inverse of y = x^2 fails it. so x = y^2 is a great example.

note: there is a reason this is not called a "function" (assuming, of course, that x and y have their usual orientations). it fails the definition of a function (see above). this is called an expression.

moved here

##### Share on other sites  as mentioned, y^2 = x is a great example.

why?  let's use the inverse: y = x^2.  think about the definition of a function, but we also know some properties, e.g. for every x, there is at most one y.  in other words, it passes the vertical line test.  as you move a vertical line, it intersects the function at only one point.  this function fails the horizontal line test.  as you move a horizontal line, it intersects the function twice.  2 different x values give the same y value.

what you're asking for is a type of expression that fails the vertical line test.  the inverse of y = x^2 fails it.  so x = y^2 is a great example.

note: there is a reason this is not called a "function" (assuming, of course, that x and y have their usual orientations).  it fails the definition of a function (see above).  this is called an expression.

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Thanks Dreamz, my sister really needed the help, and I just couldn't put it all together.

-Ax 