



 
Hi Katie, First step in determining if y is a function of x or not, is isolating y. For example, say you are given x^{2}+y^{2}=4 y^{2}=4x^{2} y=±√4x^{2} Next step is graphing. Draw a series of vertical lines. If any of these vertical lines goes through the graph more than once, it is not a function. If each vertical line goes through the graph only once, it is a function. Clearly the vertical line goes through the graph more than once so this is not a function.
On the other hand, say you are given xy3yx=0 xy3y=x y(x3)=x y=x/(x3) Looking at the graph, the vertical line crosses the graph only one time so y is a function of x. The definition of a function is for every value of x there is only one y value, that is why the vertical line test works. This graph in particular is a rational function because of the fraction. Hope this helps, Janice  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 