This graph is symmetric and has the shape of a cosine function. Because the coefficient $\displaystyle\frac{{4}}{{3}}\usepackage{cmbright}\Huge\$ is negative, this graph should be a reflection across the x-axis compared to the orientation of $\displaystyle{y}={\cos{{x}}}\usepackage{cmbright}\Huge\$ , it does. 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{{3}}{{2}}\usepackage{cmbright}\Huge\$ , the period of this function is $\displaystyle\frac{{{2}\pi}}{{\frac{{3}}{{2}}}}=\frac{{{2}\pi}}{{1}}\cdot\frac{{2}}{{3}}=\frac{{{4}\pi}}{{3}}\usepackage{cmbright}\Huge\$ . This graph has one full cycle on the interval $\displaystyle{\left[-\frac{{{2}\pi}}{{3}},\frac{{{2}\pi}}{{3}}\right]}\usepackage{cmbright}\Huge\$ , so it has the correct period also. This is a correct graph of $\displaystyle{y}=-\frac{{4}}{{3}}{\cos{{\left(\frac{{3}}{{2}}{x}\right)}}}\usepackage{cmbright}\Huge\$ .