A slider to adjust the speed of a cutom animation

I have a simple animatin that moves back and forth on the screen from left to
right. I would like to add a slider so that the user can speed up the
animation and slow it down based upon he slider. Is this possible?

The animation speeds that are selectable in the custom options are .5, 1, 2,
3. I would like it to move up in more steps than this. For example I would
like the range to be between .5 and 2 with .25 steps. Perhaps I am in over
my head. This is what I would like.

I am trying to illustrate a principle with this slide.