## 1.2. Relations and Functions

### Definition 1.2.2: Function, Domain, and Range

Let

**A**and**B**be two sets. A**function***f*from**A**to**B**is a relation between**A**and**B**such that for each*a*there is one and only one associated**A***b*. The set**B****A**is called the**domain**of the function,**B**is called its**range**.
Often a function is denoted by *y = f(x)* or simply *f(x)*,
indicating the relation *{ (x,f(x)) }*.

**Note:** James Cranston `(cranstonjames123@gmail.com)`) pointed out that occasionally
the term **codomain** is used instead of *range*, in which case the term *range* denotes the
image of the domain under the function *f* and is a subset of the codomin. We will, however, stick
with our defintion of range as the set containing all values *f(a)* and possibly more elements;
we won't use *codomain* at all.