That is an example of how strange real valued functions can be, and one that tests your understanding of continuity. It's a standard example trotted out in ele

That is an example of how strange real valued functions can be, and one that tests your understanding of continuity. It's a standard example trotted out in elementary real analysis courses along with Cantor sets, etc. If you have a good lecturer, they might make you try and come up with an example like it as an exercise before you've seen it... A good part of becoming competent at analysis is building up a grab bag of examples like this you can throw at new situations.