# 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

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