### Definitions

* Function* a mathematical relationship where each input has a single output. It is often written as f (x) where x is the input

** Domain** all possible x values, the input. (the domain of investigation)

** Range** possible y values, the output. (the range of outcomes)

** Coordinates** uniquely determines the position of a point, given by (x, y)

### 2.1. Types of functions

* Linear functions* y = m x + c

m is the gradient, c is the y intercept.

* Quadratic functions* y = ax

^{2 }+ bx + c = 0

* Axis of symmetry:* x-coordinate of the vertex: x =

^{−b}/

_{2a}

** Factorized form:** y = (x + p)(x + q)

* If* a = 1 use the factorization method (x + p)·(x + q)

* If* a ≠ 1 use the quadratic formula

* When asked excplicity* complete the square

** Vertex form:** y = a(x − h)

^{2}+ k

* Vertex:* (h, k)

#### Exponential

*f(x) = a ^{x} + c*

#### Logarithmic

*g(x) = log _{a} (x + b)*

### 2.2. Rearranging functions

* Inverse function, f^{ −1}(x)* reflection of f (x) in y = x.

* Composite function, (f ◦ g)(x)* is the combined function f of g of x.

When f (x) and g(x) are given, replace x in f (x) by g(x).