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### Definitions

### 2.1. Types of functions

#### Exponential

#### Logarithmic

### 2.2. Rearranging functions

#### Transforming functions

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**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)

** Linear functions y = mx + c**

m is the gradient, c is the y intercept.

**Parallel lines:** m_{1} = m_{2} (same gradients)

**Perpendicular lines**: m_{1}m_{2} = −1

**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)

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

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

**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).

April 14, 2024

April 14, 2024

April 14, 2024

April 14, 2024

April 14, 2024

April 14, 2024

April 14, 2024