This page aims to give an introduction to what functions in Algebra are, and how they are represented with functions notation.

### What is a Function?

A function in Algebra is a definition of a relationship between numbers.A rule that assigns, for each number/element of a certain set, say

*of set*

**a****A**.

To a unique element of a different set, say

*of set*

**b****B**.

The situation can be illustrated to show the process.

## Functions Notation

The common notation for functions in Algebra is:

*=*

**f(x)***.*

**y**Where

*represents a function involving a value*

**f(x)***.*

**x**The letter

*f*denotes the function, with an

*x*value going into the function, and a

*y*value coming out.

The letters for the values in function notation don’t have to always be

*x*and

*y*.

For example,

*=*

**f(a)***denotes a function, the value*

**b***goes in, and a value*

**a***comes out.*

**b**Also,

*doesn’t always have to be the letter that represents the function.*

**f**We can write

*=*

**h(x)***, which can denote a function, from*

**y***to*

**x***.*

**y**Sometimes you can see a function also be denoted

*:*

**f***→*

**x***.*

**y**A function from a set

**X**to a set

**Y**.

## Functions Domain and Range

Consider the function

*=*

**f(x)****3**.

*x*+ 2On a set

**X**comprising of the values

**[ 1 , 2 , 5 , 7 ]**.

*=*

**f(1)****3(1) + 2**=

**3 + 2**=

**5**

*=*

**f(2)****3(2) + 2**=

**6 + 2**=

**8**

*=*

**f(5)****3(5) + 2**=

**15 + 2**=

**17**

*=*

**f(7)****3(7) + 2**=

**21 + 2**=

**23**

Set **X** is the ‘domain’, which is the set of the values that are being put into the function.

Set **Y** is the ‘range’ or image, this set contains the values that are coming out of the function.

At times set **Y** can include some extra values, that aren’t connected to any of the values in set **X** by the relevant function.

When this happens to be the case, set **Y** is classed as the as the co-domain, which we can see illustrated below.

Along with being written as * f(x)* =

**3**.

*x*+ 2Such a standard function can also be written as

*=*

**y****3**.

*x*+ 2Seeing as it’s the

*value coming out, when an*

**y***value has gone in.*

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