What happens when there is no hose from the air pump to the Air filter?

What is your question?

My boyfriend recently had his 2001 VW Jetta Wagon in the shop. He had blown the head gasket and had it replaced, as well as an oil change, and freeze plugs replaced. After getting it back from the shop, it could not get up to speed very fast, and now almost not at all. I noticed that there is no hose from the air pump to the Air filter. The people from the shop just left it off. What kind of problems could arise from this?

What makes this problem better or worse?

Going up hills makes it worse, it goes like 10mph, at best.

How long has your 2001 Volkswagen Jetta had this problem?

A week.