The correct answer is option 2, which states that fluoride toothpaste hardens the enamel of the tooth. This is one of the primary reasons why fluoride toothpaste is recommended by dental professionals.

Enamel is the hard, outer layer of the tooth that protects the more sensitive inner layers. Over time, the acids produced by bacteria in plaque can attack the enamel, leading to tooth decay and cavities. Fluoride helps to strengthen the tooth enamel, making it more resistant to acid attacks and reducing the risk of cavities.

Option 1, preventing plaque formation, is not entirely accurate. While fluoride can help to reduce plaque buildup to some extent, its main benefit lies in strengthening the tooth enamel. Plaque can still form on teeth, even with the use of fluoride toothpaste.

Option 3, killing pathogenic bacteria, is not a direct function of fluoride. Fluoride primarily works by preventing tooth decay through enamel remineralization, rather than directly killing bacteria in the mouth.

Option 4, preventing toothache, is indirectly related to the hardening of tooth enamel. By strengthening the enamel, fluoride can help to prevent tooth decay and subsequent toothaches. However, it does not directly address or prevent toothaches.

In conclusion, the correct answer is option