Question

From the graph of g, state the intervals on which g is continuous.

Answer 1

I thought I knew, but I'm not sure of how the closed and open points affect how you state the intervals. The intervals are almost obvious as the regions of the curve, but specifically at each point where it breaks, it is critical to express the continuous region as either including ("equal to") or up to but not including the point (inequality like < or >)

Answer 2

Keep the question up... someone will know this...

Answer 3

Well i know that if there's an open and closed circle on one value of x, the limits are not the same, and it's counted as discontinuous.

Answer 4

I'll be continuous up to the limit of the point of discontinuity. e.g. it is continuous from -5 to -3, but not including -3.

Answer 5

then what about -3 to infinity?

Answer 6

i mean, negative infinity

Answer 7

What do you mean? from x=-3 to x=0 it is continuous except at the points, -3 and 0.

Answer 8

You can use inequality symbols, > < or interval notation to name the intervals. (-3, 0), e.g. would be interval notation for -3 < x < 0 where the curve is continuous.

Answer 9

yea that's what i meant, sorry i confused domain and range. But 0 is the asymptote right? does that mean after -3 to 0 that the function is still continuous after the asymptote or what?

Answer 10

And then from (0, 3) or 0 < x < 3, there is an interval of continuity, etc.

Answer 11

(3,5) right?

Answer 12

Yes, it picks up being continuous again after that point of discontinuity.

Answer 13

You might even be able to say (3, 5] to show that it is defined at x=5.

Answer 14

In the beginning, it has two closed circles, so would the interval notation be written as [-5,-3]?
And yes, that's how i wrote it.

Answer 15

Yes, I would use [-5, -3] for the first interval and then (-3, 0) for the next.

Answer 16

All right, thanks so much!

Answer 17

Sure. Just make sure you know how all that relates among continuity, existence of limits, and differentiability.

Answer 18

Yea we didn't learn to the extent of the second two, all we need to explain is where it's continuous, discontinuous, etc.