Transform functions to a different space Let's say I have a function $$f(x)=\frac{a}{x_0}(x-x_0)^2$$
I can plot this function on a XY plane by taking, $y=f(x)$. It's a parabola centered at $x_0$ and stretched by $a$ along the y-axis. My question is, how would I plot this function in a $x$ vs $y^2$ plane. 
I don't want a solution to that problem, I want you to point me in the right direction. I want to solve it myself. I am clueless where to begin. Or in general, how do I transform a function in $x$ vs $y$ plane to say $x$ vs $k(y)$ plane.

What you want to do is plot the function given by $k(f(x))$. This is called a composite function, denoted $k \circ f$. 
For example, if $f(x) = x$, and I want to plot this on the $x,y$-plane, then I get  a diagonal going through the origin with a slope of 1. If I want to plot this on the $x,y^2$-plane, I first let $k(y) = y^2$, then I get the composite function given by $k(f(x)) = (x)^2 = x^2$, and so the plot in $x,y^2$-plane of $f(x) = x$ is just a parabola.
