Need help with a graph: max (x-F,0)

[DeezNutz3]

Hi,
I haven't dealt with max and min graphs in probabley about 4 years.
This is an application of the debt versus equity topic.
Suppose a firm's business activities generate a random income of $x. Suppose a firm funds its
activities by selling one each of two sorts of claims (or securities). An investor who buys the first type
earns an income (or return) of:
min(x; F)
An investor who buys the second gets a return of:
max(x - F; 0)
Here, x is random, meaning that it is sometimes small and sometimes large and F is fixed, does
not vary. In the exercise, suppose F=$500.
a)(5p) Draw a graph of the return that an investor gets for each claim. Put the random income x
on the x axis and the investor's return on the y axis.

Now our teacher drew the min graph..it slopes upward at a 45 degree angle from the origin to the point (500,500) where it levels out. I would appreciate any help.
Thanks,
Donny

[Darryl_P]

Consider 2 cases:

1) x<500

In this case min(x,500) always equals x, so you simply draw the line y=x on this interval


2) x>=500

In this case min(x,500) always equals 500 so you just draw the line y=500 which is horizontal.