## Precalculus (6th Edition) Blitzer

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: $y=x^2$
Looking at the graphs, we find that the following order holds between the functions from the most slowly to most rapidly increasing:$$\ln x < \sqrt{x} < x < x^2 < e^x < x^x$$