Functions

Functions
A function is a rule which indicates an operation to perform.
e.g. if f(x) = x² + 3

f(2) = 2² + 3 = 7   (i.e. replace x with 2)

Functions can be graphed. For example, the graph of f(x) = 1/x is as follows:

This is the same graph as y = 1/x, although the y axis is f(x) instead of y.

Types of graphs
The graph of y = k/x (f(x) = k/x) is known as a hyperbola. Asymptotes are lines on a graph which the graph gets very close to, but never touches. Therefore in the case of y = 1/x, the x and y axes are asymptotes.
Parabolas are graphs of the form y = ax² +…