Why don't graphing tools represent holes in a graph?

Question

Why don't graphing tools represent holes in the graph of a function? A hole at a point in a graph is point where function is not defined. Suppose there is a function

$$\frac{x}{\sqrt{x+1}-1}$$

Its should be like this

But online tools and even my android graphing tool app shows graph like this

What I'm saying is that, apart from a circle, there must be some sort of marks representing that the function is not defined here.

Answer 1

Programs/apps don't usually (if ever) show the hole because it is very small. It's just one point on the graph. Less than a pixel in size, making it impossible to actually show it on your screen.

Now, as for why these programs don't indicate where point-discontinuities are? I don't know. You'd have to talk to the developer of the program. I suppose these apps could implement a way of indicating it to the user. There are ways of doing it yourself, but you'd have to symbolically program your own function/method in the language (if the app is actually a programming language).

Answer 2

Looking for gaps in the definition would require symbolic manipulation of the expression. Graphing requires only evaluating the function at a few points