1 Attachment(s)

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)

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**.

Re: The function is defined: why?