Axon Posted October 12, 2005 Share Posted October 12, 2005 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! Link to comment Share on other sites More sharing options...
loeakaodas Posted October 12, 2005 Share Posted October 12, 2005 x=3y^2 Link to comment Share on other sites More sharing options...
Guest Posted October 12, 2005 Share Posted October 12, 2005 Yeah, instead of having y = ax^2 + bx + x, just replace the y's with x's. Link to comment Share on other sites More sharing options...
dreamz Veteran Posted October 12, 2005 Veteran Share Posted October 12, 2005 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 Link to comment Share on other sites More sharing options...
Axon Posted October 12, 2005 Author Share Posted October 12, 2005 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. 586662113[/snapback] Thanks Dreamz, my sister really needed the help, and I just couldn't put it all together. -Ax Link to comment Share on other sites More sharing options...
Recommended Posts