Because the high point is $\displaystyle{\left({2}\pi,{5}\right)}\usepackage{cmbright}\Huge\$ , the height of the hill is 5. This is the amplitude of the function that was graphed. The amplitude of $\displaystyle{y}={5}{\sin{{\left(\frac{{1}}{{4}}{x}\right)}}}\usepackage{cmbright}\Huge\$ is also 5.

The length of one cycle is $\displaystyle{8}\pi\usepackage{cmbright}\Huge\$ . This is equal to the period of the function that was graphed. On the other hand, the period of $\displaystyle{y}={5}{\sin{{\left(\frac{{1}}{{4}}{x}\right)}}}\usepackage{cmbright}\Huge\$ is $\displaystyle\frac{{{2}\pi}}{{\frac{{1}}{{4}}}}={8}\pi\usepackage{cmbright}\Huge\$ . So this could be the function that was graphed.