Which of the following functions represent a travelling wave

Of all the functions $e^{-(x-vt{)}^2}$is finite every where continuous and obeys the equation $\frac{{\mathrm{\partial }}^{2}y}{\mathrm{\partial }{t}^2}=v^2\frac{{\mathrm{\partial }}^{2}y}{\mathrm{\partial }{x}^2}$
Hence ' $e^{-(x-vt{)}^2}$ ' represents travelling wave