Question

Determine if each function is continuous. If the function is not continuous, find the x-axis location of and classify each discontinuity.

Answer 1

\[f(x)=\frac{ x+1 }{ x^2-x-2 }\]

Answer 2

P.D.: 2,-1

Answer 3

This is where factoring the denominator might come in handy.

Answer 4

the (x+1) cancel out right?

Answer 5

Okay, you seem to have gotten it... now to classify...
If a certain point of discontinuity makes the denominator and ONLY the denominator zero, then it is an infinite discontinuity.

On the other hand, if a certain point of discontinuity makes BOTH the numerator and denominator zero, then it is a removable discontinuity (or a hole).

Answer 6

I think there is a hole at x=1?

Answer 7

x = 1 is not even a point of discontinuity... check the P.D's you gave me :)

Answer 8

the hole is at x=-1? but then the equation would be 0/(x-2)

Answer 9

hole is at x = -1
because at x = -1, both the numerator and denominator are zero :)

Answer 10

So it's a removable discontinuity.

Answer 11

Yup. And the other one, x = 2 ?

Answer 12

? umm they're both removable?

Answer 13

or is that the x-axis location?

Answer 14

No... I said... a P.D. would be removable if it makes BOTH the numerator and denominator zero ... so check

Answer 15

x=2 only makes the denominator 0

Answer 16

So... is it a removable discontinuity?

Answer 17

No

Answer 18

Then what is it...?

Answer 19

So it's an infinite discontinuity right?

Answer 20

Yup.

Answer 21

when they say x-axis location, would that be x=2?

Answer 22

Yes.

Answer 23

alright once again thank you, that was my last question, i can finish the rest xD

Answer 24

Awesome :)