### Function Types

A function has only one output for each input.
The set of all inputs of a function is called the domain.
The set of all outputs is called the range
Every input must has exactly one output.

#### Independent and Dependent Variables

y = x2 + 2
x is called the input variable or independent variable (x-axis)
y is called the output variable or dependent variable (y-axis)
Whatever the type of correspondence between the two variables we are always interested in the dependent variable.

#### Vertical Line Test

Functions are best described by plotting the co-ordinates of the input and output variables onto a graph
Here is f(x) - x(2) + 2 displayed as a graph
SS

You can use the vertical line test to decide if a graph represents a functions or not
The graph represents a function if any vertical line drawn only touches the line at one point
These lines represent functions

#### Relations

These lines do not represent functions and are just called relations

Splines
These are where data points are connected by a series of curves of assumed shape

Monotonic