Question

On which of the following intervals is f continuous?

Answer 1

(-4,0)
[3,5]
[5,8]
(3,5)
[-1,3]

Answer 2

I was pretty sure it was [-1,3] at first, but now I'm doubting myself.

Answer 3

it's not [-1,3] because there's a hole at x = -1

Answer 4

See, that's why I got to doubting. But I don't see any of those points that are also defined at c, so I'm confused.

Answer 5

what do you mean defined at c?

Answer 6

Our book says that a point is continuous is lim f(x) = f(c) as x-->(c)

Answer 7

ah i see what you mean now

Answer 8

ex: a point is continuous at x = 2 if

\[\Large \lim_{x\to2}f(x) = f(2)\]

Answer 9

True

Answer 10

so does this clear up some confusion?

Answer 11

I thought I did have that concept, but looking at those intervals, I'm confused. I know for sure it's not the intervals [3,5] because that is Infinite Discontinuity or [5,8], because that is a Removable Discontinuity. If you say it isn't [-1,3], that only leaves (-4,0) or (3,5)

Answer 12

And (-4,0) has two holes, am I right?

Answer 13

(-4,0) only has one hole and that's at x = -1

Answer 14

remember (-4,0) means "the interval from -4 to 0, but EXCLUDE -4 and EXCLUDE 0 from the interval"

Answer 15

Oh, yes. True. So then, I guess it must be (3,5) since the points containing the asymptote and the removed point are excluded?

Answer 16

exactly

Answer 17

we're considering numbers close to 3, but not 3 itself

Answer 18

Great, thanks jim. You were a help.

Answer 19

you're welcome