Question

Help with jump discontinuities: Give the value of x where f(x)=(x^2-4)/(x^2+x-2) has a jump discontinuity.

Answer 1

Factoring it out, I get [(x+2)(x-2)]/[(x+2)(x-1)]. How do I determine from here what value will make it a jump?

Answer 2

a jump is what you do when somethings been removed, and you have to jump over the hole, right?

Answer 3

Which, btw, reduces to (x-2)/(x-1)

Answer 4

Yes, true.

Answer 5

you already posted the "removed" version of it, the reduced version of it; what did you remove?

Answer 6

x=-2

Answer 7

correct, since you were able to remove that from zeroing out the denominator, it creates a hole that can be jumped; the other one that is left creates a vertical asymptote

Answer 8

So is it x=-1 then? Positive 1 would make it an infinite discontinuity, I know.

Answer 9

the simplified version is an equivalent, but not equal, construction. in the original setup, x=-2 is a restricted value; it makes the bottom go zero. By removing the offending factor, you created a hole a x=-2

Answer 10

Yes. I guess I'm just getting tripped up on how to figure out exactly what to look for with a jump discontinuity. I seem to grasp infinite and removable just fine.

Answer 11

you look for the factors that can be removed thru simplification. If it can be removed, then there is a hole that can be jumped over

Answer 12

Well (x+2) was removed, but x=-2 is already the removable discontinuity.

Answer 13

are you looking for the value that the function would produce @x=-2 perhaps?

Answer 14

the limit as x approaches -2 from the left and right?

Answer 15

Hmm... so I'm looking for a value that would make the entire function equal -2 you're saying?

Answer 16

no.

Im trying to figure out if ive misread your question :)

a removable discontinuity is called by many names. Hole, jump, removable ....

the factors that can be removed from the function are the places were these discontinuities exist. There is no y value for them in the original function to begin with.

so x=-2 is a jump

Answer 17

Oh. In some questions, they ask us to find the jump discontinuity, in others they ask for the removable discontinuity. So you're saying they're the same?

Answer 18

they are the same

Answer 19

Ah, well ok, that seems simple enough. Ok, well thanks for your help. I actually have to get ready to leave for school here.

Answer 20

good luck ;)

Answer 21

Thanks.