Scala heap implementation
Writing utility classes is hard enough without reinventing everything from scratch each time. Whenever possible, class authors should take advantage of available tools. In this case, Scala has a trait for ordering objects in a collection: scala.math.Ordering and it should be used for the compareFunction which will undoubtedly require some adjustment of the code.

For the most part, the code is well laid out and easy to follow. Good job! Note that standard indentation for Scala code is two spaces. It's hard to tell if the four space indentation is what is used in the code, or if it was an artifact of transferring the code into this question.

While Scala pattern matching is a great tool, it is possible to over user it. I think that using it in the pop method is not just overkill, but also results in code that is harder to read. I would write it like this:

def pop: Option[T] =  match {
  if (heapRepresentation.isEmpty) None
  else {
    val firstValue = heapRepresentation(0)
    if (heapRepresentation.size == 1) {
       heapRepresentation.remove(0)
    }
    else {
      swap(0, lastIndex)
      heapRepresentation.remove(lastIndex)
      bubbleDown(0)
    }
    Some(firstValue)
  }
}