Whenever I'm doing a question on curves, and I am given the equation without the graph I can reasonably visualise in my head what that graph would look like, and for the more complicated equations, I can just put some values in and figure it out.
However, I can't do this for parametric equations and it puts me off answering the question if I don't know what the graph would look like. if given a parametric equation in the form:
$x = f(t)$
$y = g(t)$
How can i tell what the graph would look like without having to start messing on with plotting points or algebraic manipulation, it doesn't have to be exact, just the generalised shape, (i.e. is it a circle? in what quadrant? Is it a quadratic curve? u or n? Is it a trigonometric graph?) and stuff like that so I can get a general idea for what I'm dealing with. thanks in advance. (this is for A-level questions if that helps at all)