This graph has the shape of a cosine function reflected over the x-axis. The amplitude of this graph and $\displaystyle{y}=-{3}{\cos{{\left(\frac{{1}}{{2}}{x}\right)}}}\usepackage{cmbright}\Huge\$ is 3.

This graph has one cycle on the interval $\displaystyle{\left[-{2}\pi,{2}\pi\right]}\usepackage{cmbright}\Huge\$ , so it has a period of $\displaystyle{4}\pi\usepackage{cmbright}\Huge\$ . The function $\displaystyle{y}=-{3}{\cos{{\left(\frac{{1}}{{2}}{x}\right)}}}\usepackage{cmbright}\Huge\$ has a period equal to $\displaystyle\frac{{{2}\pi}}{{\left|\frac{{1}}{{2}}\right|}}=\frac{{{2}\pi}}{{1}}\cdot\frac{{2}}{{1}}={4}\pi\usepackage{cmbright}\Huge\$ .

The effect of the negative sign is to replace y-values by their opposites. So the graph of $\displaystyle{y}={3}{\cos{{\left(\frac{{1}}{{2}}{x}\right)}}}\usepackage{cmbright}\Huge\$ gets reflected over the x-axis to become the graph of $\displaystyle{y}=-{3}{\cos{{\left(\frac{{1}}{{2}}{x}\right)}}}\usepackage{cmbright}\Huge\$ . So the graph and the function match.