A function is a rule that maps one number, the input (x) onto an other, the output (y).
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
The following graph represents a cubic function and represents the following formula:
y = x³ – 7x +2