Because the high point is $\displaystyle{\left({0},{4}\right)}\usepackage{cmbright}\Huge\$ , the height of the hill is 4. This is the amplitude of the function that was graphed. The amplitude of $\displaystyle{y}={4}\cdot{\cos{{5}}}{x}\usepackage{cmbright}\Huge\$ is also 4.

The length of one cycle is $\displaystyle\frac{{{2}\pi}}{{5}}\usepackage{cmbright}\Huge\$ . This is equal to the period of the function that was graphed. Now $\displaystyle{y}={4}\cdot{\cos{{5}}}{x}\usepackage{cmbright}\Huge\$ also has a period equal to $\displaystyle\frac{{{2}\pi}}{{5}}\usepackage{cmbright}\Huge\$ . So this could be the function that was graphed.