What Are Functions? A Quick Recap

In science and mathematics, we often explore how one quantity depends on another. A function is a precise rule that links every input value to exactly one output value.

Function

A relationship between two variables where each input value produces exactly one output value. We often write this as $f (x)$ , where $x$ is the input.

Think of a function like a machine: you put something in, the machine processes it, and one specific result comes out. For example:

Put in a temperature in Celsius → get out a temperature in Fahrenheit
Put in a time value → get out the height of a projectile
Put in a mass of substance → get out the volume it occupies

Analogy

Imagine a vending machine. You press button B3 and you always get the same snack — no surprises. That's a function: one input, one predictable output. If pressing B3 sometimes gave you crisps and sometimes gave you nothing, that would not be a function!

In MYP Sciences, functions appear everywhere — from growth curves in biology to distance-time graphs in physics to reaction rate graphs in chemistry. Understanding how to describe and limit a function using domain and range helps us model real-world situations accurately.

Introducing Domain

Domain

The domain of a function is the complete set of all possible input values (usually $x$ -values) for which the function is defined and makes sense.

In pure mathematics, we often allow any real number as an input. But in science, our inputs must be realistic. For example:

Time cannot be negative (you can't go back before the experiment started)
A population of bacteria cannot be a fraction of an organism
The concentration of a solution must be between 0 and the maximum possible value

This is why scientists must always think carefully about what input values are meaningful in the real world — not just what is mathematically possible.

How to write the domain:
We can express the domain in several ways:

Inequality notation: $0 \leq x \leq 100$
Set notation: $x \in R : 0 \leq x \leq 100$
Interval notation: $[0, 100]$

Note

At MYP level, inequality notation and plain English descriptions are perfectly acceptable. For example: "x can be any value from 0 to 100, inclusive."

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