# Plotting curved graphs

**Functions**

A** function** is a rule that maps one number, the input (*x*) onto an other, the output (*y*).

**Non-linear functions**

A non-linear function is where the graph displaying the function is curved and therefore not a straight line. An example of a non-linear function is as follows:

*y* = *x*² + 1

*y* = 3 + 2³

Non-linear functions can be plotted as a graph using a graphic calculator or a computer.

**Using a table of values**

The following function is plotted onto a table to help to display on a graph:

*y* = *x*² – 3 (use the values of *x* between -3 and 3.

The following are the coordinates of the graph:

*x*: -3, -2, -1, 0, 1, 2, 3

*y* = *x*² – 3: 6, 1, -2, -3, 1, 6

These then provide the following co-ordinates:

(-3, 6), (-2, 1), (-1, -2), (0, -3), (1, -2), (2, 1), (3, 6)

These plot then will create the following graph:

Points to note:

- The shape of the graph is called a
**parabola**(it is always symmetrical with a minimum or maximum point) - This is the characteristic of a
**quadratic function**

**Cubic graph**

The following graph represents a cubic function and represents the following formula:

*y* = *x³* – 7*x* +2