The table represents the relationship between favorite activities of teachers on different subject classes.
We know that for a relationship to be a function, a particular element on the Domain (in our case the subject the teachers teach) must associate with one and only one element in the Range (in our case the favorite activity). So we are particularly interested in finding if the repeated subjects relate with the same of different hobbies.
we cannot accept an element in the domain connecting with more than one element in the Range.
We notice that there are only two subjects repeated : English and Math.
and the great thing is that both English are connected to the same activity: "Wave surfing", so for this the relationship is still a true function. For the Math subject we are also lucky that the math teachers seem to prefer "Rock climbing". So the relationship IS a Function.
We are not somuch concerned with the other (non-repeated) subjects, since there is only one appearance of them in the relatonship.
so the function we define as the following pairs:
(Math, rock climbing); (English, Wave surfing), (History, Play cards), (Gym, Play cards), (spanish, Reading Books), (Physics, Wind surfing)
We gave the function in pair form.
