Greetings guys

I'm solving an assignment for class tomorrow and have to verify that this relation is a function.

The relation f in real is given by

xfy <=> (y(2x-3)-3x=y(x^2-2x)-5x^2)

AFAIK:

Function**:** A function is a set of ordered pairs in which each *x*-element has only ONE *y*-element associated with it.

So:

I decided to isolate y in the relation:

(y(2x-3)-3x=y(x^2-2x)-5x^2) <=>

2xy-3y-3x=y(x^2-2x)-5x^2) <=>

Divides with y on both sides:

4x-3-3x/y=x^2-(5x^2)/y <=>4x-3-x^2=3x/y - (5x^2)/y

y(4x-3-x^2)=3x-5x^2<=>y=[3x-5x^2]/[4x-3-x^2]

When i do a graph for y. I see that the relation isnt a function, since the relation shares coordinates on x about =[0;2] (*the exact value doesnt matter)