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.
You may use horizontal lines to verify that a function is injective.
If every horizontal line intersect the graph at most once the function is injective
Otherwise it is not injective