Based on the description provided of the protist having "long lash-like appendages," it is likely that these appendages are flagella. Flagella typically move in a whip-like or undulating motion, which is often described as moving back and forth like a wagging tail to actively propel the organism forward.
Therefore, the correct response would be:
The appendages of this protist will move back and forth like a wagging tail to actively propel the protist forward.