General Mathematics is one of the core subjects of Senior High School Students. In the earlier part of this subject, functions will be introduced.

In a real-life setting, some people might say it is not commonly being observed. It is not true. In fact, it exists, we can't just notice it sometimes. Let's take the following for example.

Let's say you're working as a tutor. Now think about the income you will earn from it. Let's say you get 200 pesos for tutoring math. The amount of money you get, which is the output, will depend on the number of hours you tutored a particular student (input).

That example is just a simple function. It is not just about the money. The functions are used to figure out how things change.

**What are functions?**

Functions serve as a cornerstone for understanding the relationships between domains.

To better understand its meaning, here's a comparison with it to relation.

**Differentiate relation with function**

**Relation**

It is any set of ordered pairs.

Domain, or the first elements of ordered pairs, is the set ofx-values. It is otherwise known as theinput.

Range, or the second elements of ordered pairs, is the set ofy-values. It is otherwise known as theoutput, which is dependent on the input.

**Function**

In its simplest term, it is a relation where every element in the domain corresponds to only one value in the range. Each value of x relates to only one value of y.

**Important Keynote:** *one-to-one relationship*

**Examples:**

x: 1 2 3 4 5

y: 6 12 18 24 30

1 relates to 6; 2 relates to 12; and so on. No values of y have the same values of x.

z = {(4,1), (3,9), (2,8), (7,5)}

Using diagrams, we can also identify which is a function and which is just a mere relation.This one is a function, too, because each value of x relates exactly to only one value of y.

** The first one is a function** since each element in the domain relates to a distinct element in the range. However,

*but a mere relation because there is a value of x that relates to more than one value of y.*

**the second one is not a function****Remember:** *All functions are relations.* However, a relation can only be a function if all the values of the domain (x) correspond to exactly one value of the range (y).