Animating separate object through keyframe

I have got my head around generating 3D object using the mathematical mesh tool <shift A mesh>Extra objects>Math Function>

I want to animate the plotting process for a 3D function

I can increment a parameter (u) to generate the plots at various points and so I have been going through the process of

1 Create Frame with object in it
2 Make it a key frame
3 Go to 10 frames on
4 create another object with my parameter incremented (I think this is my problem)
5 Go back to 1

I think the issue is that I am making lots of objects instead of animating just one.

Can anyone point me to a method of approaching this? Perhaps a similar tutorial?