IB Maths AI 2.2 Notes

This page contains our IB Maths AI notes for 2.2. By reading each one of these notes, you will fully cover the content for IB Maths AI 'Introduction to functions'.

All Topic 2 Sub-topics 2.1: Forms Of Lines 2.2: Introduction To Functions 2.3: Introduction To Modelling Functions 2.4: Modelling Applications (HL)2.5: Further functions (HL)2.6: Graph transformations (HL)2.7: Advanced modelling functions (HL)2.8: Logarithmic graphs

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Chapters

1. Functions

2. Domain & range

3. Graphs of functions

4. Intercepts & roots

5. Inverse functions

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Functions

In this topic, functions are used as mathematical models, then studied through their graphs, key features, compositions, inverses, and important families such as quadratics, reciprocal functions, rational functions, exponentials and logarithms.

A function is a rule that takes each input and gives exactly one output. If a function is called $f$ , then writing $f(x)$ means the output of the function $f$ when the input is $x$ .

Math Topic 2 subTopic 2 notes image 1

If $f(x)=2x+3$ , solve $f(5)$ .
So, substitute $x=5$ .
$f(5)=2(5)+3=13$ .
So when the input is $5$ , the output is $13$ .

A function can be used as a mathematical model. For example, $v(t)$ could represent velocity as a function of time, or $C(n)$ could represent cost as a function of the number of items bought.

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