I am reading about mathematical representation of curves and have come across following points which I can't seem to understand :
1) Why Explicit representation cannot be used to represent closed and multi-value curves and why the implicit representation can do so?
2) Why parametric representation is preferred for rendering the curves?
3) Why it is not easy to find out if a given point lies on the curve when using the parametric representation?
Simple visual examples would be beneficial as I am really starting out learning all this and might not understand too much of the related maths jargon!
1) If by explicit representation you mean $y=f(x)$ then the main thing is that closed and multivalued curves are not function (a function has one output to each input by the definition) and therefore cannot be used in these cases.
2) because this is relatively simple way to express any curve.
3) because $(f(t),g(t))=(a,b)$ is simultaneous solution of two not necessarily simple equations.