April 14, 2024

Table of contents & cheatsheet (FUNCTIONS)

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.

Linear functions
Linear functions 1

Quadratic functions y = ax+ bx + c = 0

Axis of symmetry: x-coordinate of the vertex: x = −b/2a

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

Quadraticfunctions

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) = ax + c

Exponential

Logarithmic

g(x) = loga (x + b)

Logarithmic

2.2. Rearranging functions

Inverse function, f −1(x) reflection of f (x) in y = x.

 

Inverse function

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).

Transforming functions

Transforming functions