Graphing non-linear functions
Example:
The motion of a defense aircraft is following a particular path in the sky given by its cartesian coordinates as in the following table.
| x | y |
| -3 | 5 |
| -2 | 0 |
| -1 | -3 |
| 0 | -4 |
| 2 | -0 |
| 3 | 5 |
Another pilot wants to view the motion of the aircraft graphically. The motion of the aircraft is a
non-linear one and can be graphed as follows.
The above graph is called a parabola.
The parabola is represented by the following non-linear function.
y =x2 - 4
The lowest point (0, -4) is the vertex point of the above parabola.
Once again, by viewing the above graph, one can always locate the position of the aircraft and predict its path with its
cartesian coordinates in the given domain and range. The graph has been drawn within the domain of [-3,3] and its range is [-4,5].
Example:
Graph the function y= x3 - x with x values in the domain of [-2 2].
Solution:
The above function needs more data points since it is a polynomial function of 3rd degree. We choose the values of x in the domain [-2 2] and find out the corresponding values of
y using the above function. The values ofx and y are tabulated as below.
| x | y |
| -2 | -6 |
| -1 | 0 |
| -0.5 | -0.375 |
| 0 | 0 |
| 0.5 | -0.375 |
| 1 | 0 |
| 2 | 6 |
The graph of the data points in the above table is shown below:
The above graph passes through the origin and when x increases beyond 1, y also increases almost
linearly. When x decreases beyond 1, y also decreases almost linearly. When x value lies between -1 and
1, the y value changes in a non-linear way.
Some spreadsheet packages (e.g., MS Excel) provide the polynomial that best fits a set of data values from a function.