I have two functions, for example y=x and y=x^2. Is there a way to rotate the second function, y=x^2, 45 degrees clockwise so that the translated second function (previously y=x^2) is seen just as if the first function was the x-axis?

Question

I have two functions, for example y=x and y=x^2. Is there a way to rotate the second function, y=x^2,  45 degrees  clockwise so that the translated second function (previously y=x^2) is seen just as if the first function was the x-axis?

anonymous · Answer

And more generally, is there a way to morph a Cartesian graph so that the x-axis is essentially a function in the old, unmorphed Cartesian graph?

anonymous · Answer

if the second function is a linear function.. such as y=x, you can picture it in your head..
I don't know of any graphing utilities that do this because it seems un-useful.

Plus, it's limited to linear functions.. how are you going to change the x-axis into a parabola?