Hello, I am currently studying a section in my math book entitled "Increasing and Decreasing Functions," but my inconvience dwells in my contention with what the author states about a constant function.

Here is a picture of the figure they give me in the book

2011-07-01_10-12-23_898.jpg picture by Bashyboy - Photobucket
The rule, in the book, states that "a function f is constant on an interval if, for any Xsub1 and Xsub2 in the interval, f(Xsub1)=f(Xsub2).

So, when I try to apply this rule to our figure, I run in to the fact that segment of the constant part of the function begins at (0,1) and ends at (2,1). I know definitively that 0 does not equal 2, so I am able to deduce that I am obviously wrong in my understanding of this rule. I appreciate any whom try to answer.