Not sure if you're familiar with 'linear functions', so I'll try my best to explain.
Say we have two variables, one dependent on the other. In our case, cost is dependent on diameter, i.e. [tex]C[/tex] depends on [tex]d[/tex]. The diameter, [tex]d[/tex] in itself does not depend upon anything. In other words, we denote [tex]C(d)[/tex] as a function [tex]C[/tex] that depends on [tex]d[/tex].
We say that a function is linear, if it can be expressed like this:
[tex]C(d)=gradient\times d+number[/tex]
In this case, our gradient is (rise over run) 200, and that number on the right is 400.
Graphically, linear functions are exactly what they are - straight lines.
With a positive gradient, the line will extend from the bottom left of the page all the way to the top right.
Smaller values of the diameter, [tex]d[/tex], will give us smaller values of the cost, [tex]C[/tex].
Larger values of the diameter, [tex]d[/tex], will give us larger values of the cost, [tex]C[/tex].
Range of a function is defined by the minimum and maximum values the dependent variable, [tex]C[/tex], can take based on the values of
