Because the low point is $\displaystyle{\left({1},-{5}\right)}\usepackage{cmbright}\Huge\$ , the depth of the valley is 5. This is the amplitude of the function that was graphed. The amplitude of $\displaystyle{y}={5}\cdot{\cos{\pi}}{x}\usepackage{cmbright}\Huge\$ is also 5.

The length of one cycle is 2. This is equal to the period of the function that was graphed. Now $\displaystyle{y}={5}\cdot{\cos{\pi}}{x}\usepackage{cmbright}\Huge\$ also has a period equal to $\displaystyle\frac{{{2}\pi}}{{\pi}}={2}\usepackage{cmbright}\Huge\$ . When $\displaystyle{x}={1}\usepackage{cmbright}\Huge\$ , the value of $\displaystyle{y}={5}{\cos{\pi}}={5}{\left(-{1}\right)}=-{5}\usepackage{cmbright}\Huge\$ . So it does pass through $\displaystyle{\left({1},-{5}\right)}\usepackage{cmbright}\Huge\$ . So this could be the function that was graphed.