Given the functions:

$$y=\cfrac{1}{x}$$

$$y={x}^{2}$$

$$y={x}^{3}$$

$$y=\left|x\right|$$

Which of the following statements are true?

I. All of these functions are increasing over the interval $x>0$.

II. Two of these functions are even functions.

III. Three of the functions have a domain of all real numbers.