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?
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why don't you do $f(x) = x^3?$ Illustrates some of the issues well. – Will Jagy Dec 07 '15 at 03:17
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To understand this you should try using the graph of $y=\sqrt {x}$ as an example. – AnotherPerson Dec 07 '15 at 03:19