This function and the graphed function both have 5 as the amplitude. However, they have different periods. The graphed function has a period of $\displaystyle{8}\pi\usepackage{cmbright}\Huge\$ , while $\displaystyle{y}={5}{\sin{{4}}}{x}\usepackage{cmbright}\Huge\$ has a period of $\displaystyle\frac{{{2}\pi}}{{4}}=\frac{\pi}{{2}}\usepackage{cmbright}\Huge\$ . The correct answer is $\displaystyle{y}={5}{\sin{{\left(\frac{{1}}{{4}}{x}\right)}}}\usepackage{cmbright}\Huge\$ .