Answer
The red graph: $y=x$
The blue graph: $y=\sqrt{x}$
The green graph: $y=e^x$
The purple graph: $y=\ln x$
The black graph: $y=x^x$
The orange graph: $y=x^2$
Work Step by Step
Looking at the graphs, we find that the following order holds between the functions from the most slowly to most rapidly increasing:$$\ln x < \sqrt{x} < x < x^2 < e^x < x^x$$
