## Fun Functions

f(x) = 3cos(x) + 2x – 4

f(x) = x3 – 4x2 + 3

Confused? Those of us who have learned advanced mathematics may be more familiar with what is above, while it may be just more gibberish to those of us who have not learnt that yet.

As complicated as it seems, those two lines, known as functions, are nothing more than just a statement that tells us the relationship between two things, or variables. It’s really just like your normal line graph.

There’s quite a bit of fun that we can play with these mathematical functions. Yes, I probably sound crazy for suggesting that math can be fun… but hear me out! Come along and let’s see what fun functions can bring us.

f(x) = x + 1

This basically means that if x =1, then f(x) = 1+1=2. If x = 2 then f(x) = 2+1 =3. Simple, right? If we put the values into a table, and plot the points on a line graph, draw a line to connect the dots, we get something like this:

Still looks kind of boring, I know. But what if we change the function to something else? Lets try the sine function, where f(x) = sin(x). (that button that says ‘sin’ on your scientific calculator)

Repeating the same process, this time we get a wavy line!

Even more complex functions allow us to draw even more shapes. For example, using the function (x-h)2 + (y-k)2 = r2 allows us to draw a circle, size depending on what numbers we choose h, k and r to be.

Combining several functions together, some math artists have come up with incredible artwork made. Check out this website to see many different art pieces which people have made using graphs!

Ultimately, you might ask what is the importance of a function? In science, many variables are affected by other variables. Just like how when the number of predators in a food chain increases, the number of preys will likely decrease. Increase the amount of water and sunlight given to a plant, it is likely to grow taller. With every action in science, be it biology, chemistry or physics, there is a related effect.

Functions allow scientists to better understand how exactly everything works around us. It allows scientists to better predict what will happen from their observations. At the end of the day, math is very much crucial to science, and as you can see, math can create great fun and artworks too!

Written by Emily Du and Raphael Ng
Illustrated by Lee Ai Cing