calculus

[proud palm]

What conditions should I keep in mind to know if I can go from a graph written in parametric form to a Cartesian one?

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[timid gale]

what do you mean by "Cartesian one"

do you mean :
we have some function f(t)=(x(t), y(t)) or say the graph G(f, a, b, c, d) = {(x(i),y(j)) : i in [a, b], j in [c, d]} etc. you ye the point.
Now we convert this to some function of the form :
y=f(x) like we usually have. If yes, you just have to check if there's multiple values of y for some x which contradicts f (a relation) being functional. To do this look back to the original parametric : f(t) = (x(t),y(t)) and just check that is there some m, n such that x(m)=x(n) but y(m)≠y(n), geometrically it'd just mean that at some x-coordinate it has two y values, which we can't make into a function.