# The function is defined: why?

• Oct 1st 2011, 10:24 AM
raymac62
The function is defined: why?
I am looking at the graph of function f(x)=(x-1)/(x^2-1) produced by the program: "Graph" created by Ivan Johanson.

Why is this rational function defined at x = 1 as the limiting value 0.5?

Is this a convention for it to be defined as the limit? Or am I crazy? (Nerd)
• Oct 1st 2011, 10:31 AM
HallsofIvy
Re: The function is defined: why?
Well, you are only crazy if you expect a computer to be as good as your brain! What is graphed there is NOT the function you give. What is true is that
$\displaystyle \frac{x-1}{x^2-1}= \frac{x-1}{(x-1)(x+1)}$
which is not defined at x= 1 and so its graph should have no point on the vertical line at x= 1.

However, for all x except x= 1,
$\displaystyle \frac{x- 1}{(x-1)(x+1)}= \frac{1}{x+1}$
which is defined at x= 1. The computer, calculating values at a finite number of values of x, "misses" the problem at x= 1 and just graphs y= 1/(x+1).
The graph is wrong.
• Oct 1st 2011, 10:37 AM
raymac62
Re: The function is defined: why?
Thanks for clarifying.