This graph has the general shape of a cosine function, so $\displaystyle{y}={a}{\cos{{b}}}{x}\usepackage{cmbright}\Huge\$ . The amplitude is 2. The graph has the same orientation as $\displaystyle{y}={\cos{{x}}}\usepackage{cmbright}\Huge\$ , so no reflection has occurred. Therefore $\displaystyle{a}={2}\usepackage{cmbright}\Huge\$ .

Now there are four cycles that run from 0 to $\displaystyle\frac{{{8}\pi}}{{5}}\usepackage{cmbright}\Huge\$ , so the period is $\displaystyle\frac{{{2}\pi}}{{5}}\usepackage{cmbright}\Huge\$ . Since $\displaystyle\frac{{{2}\pi}}{{5}}=\frac{{{2}\pi}}{{\left|{b}\right|}}\usepackage{cmbright}\Huge\$ , the value of b could be 5. So this could be the graph of $\displaystyle{y}={2}{\cos{{5}}}{x}\usepackage{cmbright}\Huge\$ .