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Day 4: Introduction to FunctionsDescription: Introduction to Functions
Objective: Learn how a function is a set of inputs coupled together with a set of outputs to describe some relationship. Practice using a formula with a set of inputs to get an answer for EACH of teh inputs and then write them as a function.
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Introduction to Functions

A set of Inputs (to a formula) gives a set of Outputs.

Using a formula with changing or variable values

John makes 30 euro per day (for turning up) and makes an additional 9 euro for every hour that he works.

How much money does he make?

The answer of course depends on how many hours that he works.

If he works 7 hours he makes:

30 + 9 x 7

= 30 + 63

= 93

Ans: 93 euro.

John makes 30 euro per day (for turning up) and makes an additional 9 euro for every hour that he works.

If he works 12 hours he makes:

30 + 9 x 12

= 30 + 108

= 138

Ans: 138 euro

John makes 30 euro per day (for turning up) and makes an additional 9 euro for every hour that he works

So for different number of hours we get a different answer

The formula that we use to find out how much he makes is as follows:

If John works for n hours

(The letter ‘n’ represents how many hours that he works)

Then the formula for how much he makes is:

30 + 9n

Which means ’30 plus 9 times n’

Where ‘n’ means whatever the variable or changing number of hours that he works.

Using a formula with a Set of values

When we have a formula like:

30 + 9n

We can find out how much John makes for a list of different possible hours that he works.

This list of hours is called a SET

Example: N = {2,5,9,12}

SET of Input values

For EACH one of the set of input values that we have:

N = {2,5,9,12}

We can work out how much John makes using our formula: 30 + 9n

When n = 2, John makes 30 + 9(2) = 48

When n = 5, John makes 30 + 9(5) = 75

When n = 9, John makes 30 + 9(9) = 111

When n = 12, John makes 30 + 9(12) = 138

Set of input values -> Set of output values

So we have a connection between each of the input values that we have and each of the output values we have.

2 -> 48, 5->75 , 9->111 , 12->138

When a SET of input values is ‘mapped’ to a set of output values we have what is called a FUNCTION.

Functions (Domain -> Co-Domain)

Out inputs are now in a relationship with our outputs

Each input is in a couple with an output.

2 -> 48, 5->75 , 9->111 , 12->138

In the following questions I will ask you to write this relationship as a set of ordered pairs (or a set of couples)

{ (2,48), (5,75), (9,111), (12,138) }

Function Questions

1. In these questions I won’t tell you what the formula that we use means. Just how to find the output from the input.

Example:

Domain : { 1, 7, 9 }

Function : f(x) = 3x + 10

List the set of couples created by this function.

Function Questions

Domain : X = {1, 7, 9 }

Function : f(x) = 3x + 10, x ∈ X

List the set of couples created by this function.

1 -> 3(1) + 10 = 13

7 -> 31

9 -> 37

Ans: { (1,13), (7,31), (9,37) }