Graphing y=x^0 -> y=x^1 and y=x^1 -> y=(1/2)(x^2) and doing math on the shapes (just simple squares and rectangles) makes those pretty intuitive. I just see it

Graphing y=x^0 -> y=x^1 and y=x^1 -> y=(1/2)(x^2) and doing math on the shapes (just simple squares and rectangles) makes those pretty intuitive. I just see it as an extension of that.