# Can we describe Injective and non-Injective functions through intersections?

Is it true that if curves are self-intersecting, then function graph would be non injective ?

Like suppose a differential curve $\alpha(t) = (x,y) = (t^2, t^3)$ where $y=f(x) ,$ its function graph comes out as $y=x^{3/2}$ and they self-intersect and so are non injective?

Let us take another functions like $\alpha(t) = (3t/1+t^3, 3t^2+1+t^3)$ never self-intersect and they are injectives. So my question is:

Do intersections solly define a function's injectivity or non-injectivity ? What are other definitive requirements? Thanks.

• Welcome to MSE. Questions are usually received better if you give a bit more background including what you have tried and where you are stuck. This should be added to the question itself. Jul 18, 2018 at 12:09
• Please Check out the question once again i put some explanation here. I'm trying Differential Geometry and it's about curves. Jul 18, 2018 at 12:19

• $alpha(t) = t^3-4t, t^2 -4$ are not injective. $\alpha (-2)=\alpha (2)$ Jul 18, 2018 at 13:02