In the new version of blender, it doesn't seem as though there is an option for repeat motion offset on the right (or modifier, even if the cyclic modifier is already added)
How should I change my graph line to have repeat motion offset?
I don't seem to have that option for some reason. The cyclic modifier is on. 
Thank you!
I checked, but those options doesn't pop up for me for some reason on the right.
Hi Grace,
The curve needs to be active. So you need to click it on the area on the left hand side so that Blender knows which curve is active.
It can be a little confusing at times because a curve (or curves) can be selected but there might not be an active curve. The last curve you select will be the active one.
For example - if you select all the curves with `A`. They will be selected but none will be active, because they were all selected at the same time so Blender doesn't choose which one should be active. This is by design (and it's logical) but sometimes it can be confusing.
Hope that helps.
The good news is, you are probably an expert on active vs select curves now :)