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 = x² + 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 = x² – 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 = x² – 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 – 7x +2