IB

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

### 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 = mx + c

m is the gradient, c is the y intercept.

Parallel lines: m1 = m2 (same gradients)

Perpendicular lines: m1m2 = −1

Quadratic functions y = ax2 + 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) = ax + c

#### Logarithmic

g(x) = loga(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).

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