Free particle wavefunction represent a fixed profile= wavepacket?

[Outrageous]

Why the Griffiths book says : any function of x and t that depends on these variables in the special combination (x±vt) represent a wave of fixed profile, traveling in the -+x direction at speed v...
I don't really get the reason why from 2 terms of wavefunction can become only one term?

Please help.
Thanks

 

[vanhees71]

Griffiths means that your wave function is either of the form $\psi(t,x)=f(x-v t)$ or of the form $\psi(t,x)=f(x+v t)$. Obviously the shape of the wave stays the same for each time, but it's moving to the right or left, respectively.

 

[Outrageous]

Griffiths means that your wave function is either of the form $\psi(t,x)=f(x-v t)$ or of the form $\psi(t,x)=f(x+v t)$. Obviously the shape of the wave stays the same for each time, but it's moving to the right or left, respectively.

How do you know there are two form of wavefunction?
By drawing out a graph of wavefunction against x? To see they are actually two superposition of two traveling wave?
Those information are from the wave function? How do you know? Do I miss any wave knowledge? Where should I study these?