Looking at this: , represents the dividend and is just the input.

When is 1, we have our familiar rational function.

As increases, the two curves seen expand. And inversely, as decreases the curves get closer and closer to the x and y axis.

What happens when is simply 0? We'd have the function

Okay, so the function is 0 everywhere, except for . Raising the question, what is 0 divided by 0?

Some say 0, some say 1, or undefined, or indeterminate. I think most of us would probably agree on an indeterminate form.

so . We know 0 times 0 is 0. We know 1, 2, 3, pi, -1, and every real number times zero is 0.

So the value of 0/0 is indeterminate, so how would I show that on the graph?

Seeing how 1/x, 0.5/x, 0.1/x etc... gets closer and closer to the x and y axis, we'd eventually see lines coincidental to the x and y axis. Right?

It makes sense since indeterminate forms mean the value could be anything, so every value for the domain 0 would be represented, a vertical line.

What do you think about this?

( I started a thread on a similar topic on "f(x)=x^x (tetrative functions)" )