Functional Graphs

Types of Graphs

Graphs are used in various aspects of mathematics – but in the real world they can take on specific meanings
For example a linear (straight line) graph could be the path a ship needs to sail along to get from one port to another
An exponential graph () can be used to model population growth – for instance to monitor wildlife conservation projects

Recalling facts alone won’t do much for boosting your IGCSE Mathematics grade!
But being familiar with the general shapes of graphs will help you quickly recognise the sort of maths you are dealing with and features of the graph a question may refer to
Below the basic form of the five types of function (other than trig graphs) you need to recognise;
- linear ( $y = \pm x$ )
- quadratic ( $y = \pm x^{2}$ )
- cubic ( $y = \pm x^{3}$ )
- reciprocal ( $y = \pm \frac{1}{x}$ )
- exponential ( $y equals k to the power of plus-or-minus x end exponent$ )

Complete the table of values for the function $y equals x cubed minus 5 x plus 2$ . and plot the Graph using those coordinates

x	-3	-2	-1	0	1	2	3
y		4					14

If you have a scientefic calculator use the table function

TO MANUALLY CALCULATE use the following steps

for example for x = -3 column to find y you have to put/substitute -3 where there is x in the equation as shown below

use the same method for all x values to calculate your y values. Below is the completed table

x	-3	-2	-1	0	1	2	3
y	-10	4	6	2	-2	0	14