IB Maths AA 2.2 Notes

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 $x$.

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.