What is the graph of a function?
Example:
The cost of training defense people for a certain task increases with respect to the number
of people as shown in the following table.
| no. of people | cost (in $1000) |
| 5 | 5.5 |
| 10 | 10.5 |
| 15 | 15.5 |
| 20 | 20.5 |
| 25 | 25.5 |
As we have already seen in the functions station, the relationship between the cost and the
number of people is a linear one and can be represented by the following linear function.
cost = no. of people + 0.5or to use a more general form, we can write
C(n) = n + 0.5
To understand and analyze the above data in a better way, we can plot the graph of the above data as
following:
From the above graph, we can interpret that as the number of people increases, the cost also increases linearly with slope 1. If the number of people is zero, the cost is $500 which is the start up cost for setting up the training session.
Definition:
The graph of a function y = f(x) is the set of all points whose coordinates are (x, f(x)).