Illustrations of the 4 most common Functions in School Mathematics


Straight Lines

Imagine buying a cup of coffee for a friend that cost $1.50, then imagine buying a 2nd cup of coffee for another friend. Thing about how much extra you spent for that 2nd cup. Okay, buy another cup for a third friend. It total you have spent $4.50 for 3 cups of coffee. The relationship that describes how the cost increases as you buy more and more cups of coffee is called a straight line relationship or linear function.



Parabola

Consider trying to organise a Round Robin Tennis Tournament with some friends. When you first start planning the tournament, only 4 of you seem to be able to make it. Then the day before, a 5th member joins and then on the day itself, your cousin is in town and he wants to play too!

How many matches do you need to arrange so that the tournament could take place with either 4, 5 or 6 players ?

The relationship between the number of players and the number of matches to be scheduled is parabolic, or forms a parabola when visualised.



Exponential 

Take a piece of A4 paper and fold it in half. How many equal partitions do you have ? Now fold it again and again observe the partitions. Finally fold it a 3rd time, what do you notice about the partitions and how they are changing? 


The relationship between the number of folds and the number of partitions is an example of what we call exponential growth or an exponential function. Population growth is often described using this type of relationship. 

Hyperbola 

Imagine buying a chocolate slab with 12 pieces. As you leave the shop where you bought it from, you run into a friend and you decide to stop and have a chat, so that you can share it with them. Then just as you are about to divide it up, another friend walks past and you decide you don't want this person to feel left out, so now you need to divide your chocolate into three equal sections.

Then just when you thought you were finally about to start eating your chocolate, your mom comes past and says she has a real sweet tooth. You cant leave your mom out , so now you need to divide your chocolate slab into 4 equal pieces.

What do you notice about how much each person gets, as you need to share it between more and more people? What do you notice about the overall relationship between no. of people sharing and no. of pieces of chocolate you each get?





Summary 

These 4 situations paint a real life picture of the most common relationships (Mathematical Functions) that students study at high school.

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