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](https://revisiontown.com/wp-content/uploads/2023/03/Screenshot_2023-03-12-16-47-59-95_e2d5b3f32b79de1d45acd1fad96fbb0f.jpg)
![Linear functions 1](https://revisiontown.com/wp-content/uploads/2023/03/Screenshot-2023-03-12-at-5.54.38-PM.png)
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)
![Quadraticfunctions](https://revisiontown.com/wp-content/uploads/2023/03/Screenshot-2023-03-12-at-4.58.21-PM.png)
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](https://revisiontown.com/wp-content/uploads/2023/03/Screenshot-2023-03-12-at-4.58.58-PM.png)
Logarithmic
g(x) = loga (x + b)
![Logarithmic](https://revisiontown.com/wp-content/uploads/2023/03/Screenshot-2023-03-12-at-4.59.06-PM.png)
2.2. Rearranging functions
Inverse function, f −1(x) reflection of f (x) in y = x.
![Inverse function](https://revisiontown.com/wp-content/uploads/2023/03/Screenshot-2023-03-12-at-4.59.21-PM.png)
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](https://revisiontown.com/wp-content/uploads/2023/03/Screenshot-2023-03-12-at-6.30.58-PM.png)