First, this graph is symmetric and has the shape of a cosine function. Second, because $\displaystyle{a}=\frac{{4}}{{3}}\usepackage{cmbright}\Huge\$ in the equation, the amplitude is $\displaystyle\frac{{4}}{{3}}\usepackage{cmbright}\Huge\$ . Finally, because $\displaystyle{b}=\frac{{2}}{{3}}\usepackage{cmbright}\Huge\$ , the period of this function is $\displaystyle\frac{{{2}\pi}}{{\frac{{2}}{{3}}}}=\frac{{{2}\pi}}{{1}}\cdot\frac{{3}}{{2}}={3}\pi\usepackage{cmbright}\Huge\$ . This graph has one full cycle on the interval $\displaystyle{\left[-\frac{{{3}\pi}}{{2}},\frac{{{3}\pi}}{{2}}\right]}\usepackage{cmbright}\Huge\$ , so it has the correct period also. This is the correct graph of $\displaystyle{y}=\frac{{4}}{{3}}{\cos{{\left(\frac{{2}}{{3}}{x}\right)}}}\usepackage{cmbright}\Huge\$ .