how do i figure out the graph of ((x^2)-2x-3)/|x+1| without using a calculator?

Question

how do i figure out the graph of  ((x^2)-2x-3)/|x+1| without using a calculator?

anonymous · Answer

like how do i figure out that -1 is a removable discontinuity

hero · Answer

because if x = -1, then you end up with 0/0

anonymous · Answer

how do i determine if it's gonna be a removable or nonremovable discontinuity?

hero · Answer

Basically if the graph goes to infinity as a number reaches a certain value, then that is essentially a non-removable discontinuity.

In this case, the only thing that is keeping the graph discontinuous is the fact that $$x \ne -1$$

However since we can define f(x) = x - 3, we can say that f(-1) = 1 - 3 = -2 and redefine f(-1) = -2 so that the graph is continuous. We would not be able to do that with a function such as f(x) = 1/x^2 however

anonymous · Answer

why isn't f(-1)= -1-3?

hero · Answer

Watch this video. It will tell you everything you need to know http://www.youtube.com/watch?v=f1R1u3A36T0&feature=related