You may have chosen this answer because you are not familiar with the graphs of exponential functions, or you misread the answer. The graph of $\displaystyle{f{{\left({x}\right)}}}={e}\cdot{0.5}{x}\usepackage{cmbright}\Huge\$ would be linear, because the variable x is being multiplied by two constants, e and 0.5. The given graph is not a straight line.