RPMs jump when shifting

[TMalone]

My friend has a 99B Jetta, manual and it has started doing something strange. This usually occurs when it's cold, but has occurred at other times at well. What happens is when she puts it into reverse the RPMs just up to about 3K. It has also happened when shifting into 1st. The check engine light does come on and she will be taking it in to have the trouble code read but I'm concerned that she'll spend a fortune getting things done that aren't necessary. So, I guess what I would like is some guesses as to what's going on so she'll know what to expect.
Thanks!