A typical way to define a function 𝑓ff from a set 𝑆SS, called the domain of the function, to a set 𝑇TT, called the range, is that 𝑓ff is a relationship between 𝑆SS to 𝑇TT that relates one and only one member of 𝑇TT to each element of 𝑋XX. We use 𝑓(𝑥)f(x)f(x) to stand for the element of 𝑇TT that is related to the element 𝑥xx of 𝑆SS. If we wanted to make our definition more precise, we could substitute the word “relation” for the word “relationship” and we would have a more precise definition. For our purposes, you can choose whichever definition you prefer. However, in any case, there is a relation associated with each function. As we said above, the relation of a function 𝑓:𝑆→𝑇f:S→Tf: S → T (which is the standard shorthand for “𝑓ff is a function from 𝑆SS to 𝑇TT” and is usually read as 𝑓ff maps 𝑆SS to 𝑇TT) is the set of all ordered pairs (𝑥,𝑓(𝑥))(x,f(x))(x, f(x)) such that 𝑥xx is in 𝑆SS.