Im so confused please help. I believe this is from Goldstein's classical mechanics #1.21

Problem-2 (10 points). The electromagnetic field is invariant under a gauge transformation of the scalar and vector potential given by A - A + Vy(r,t) 1 dub b - c dt where, w is an arbitrary but differentiable function. What effect does this gauge transformation have on the Lagrangian of a particle moving in the electromagnetic field? Is the motion affected