Avery took a wave motion rope and waved it sideways once. What kind of wave did Avery create, transverse, longitudinal, or a pulse?

transverse wave.

Explanation:

In a wave motion rope, the particles of the rope move in the perpendicular direction to the actual wave, so this is a transverse wave.  (we have a longitudinal wave when the movement of the particles is in the same direction than the wave propagation, an example of this is the waves in the surface of the water when you throw a rock in)

Now, the fact that he waved it only once does not mean that this is a pulse if the other end of the rope is connected to a fixed point when the wave reaches that point will be reflected (losing a bit of amplitude, but we still will have a wave)

so the correct option is a transverse wave.