Graph Sketching and Transformations

Question

Sketch the following

$$y = f(x)$$ $$y^2 = f(x)$$ $$y = f(x^2)$$ $$y^2 = f(x^2)$$

Obviously you can't sketch these, but how does each graph differ from the first one, i.e. how are they transformed and is there a general idea behind all of these?