So I will answer it, but please forgive me for resorting to some cheap ploys to hold everyone's attention. First the basics. As you said, when interest rates rise, bonds fall, as do bond funds. However, not all bond funds are created equal. The longer a bond fund's duration, the farther it may plummet.
Duration is the average maturity of the fund.
If your bond fund's duration were longer than 4 years, its value would immediately fall. If, however, you owned a bond fund with a duration of less than 4 years, the situation would be slightly different. Yes, the bond fund would still fall in value, but not by as much as a long-duration fund. For this fund, the gain in the yields would offset the loss in bond values, and you would make money over the 4 years. Consequently, shorter duration bond funds are far less risky for you to invest in than long duration funds.