Question

Calculus question:
Find all values of a such that f is continuous on (-infinity, +infinity)
f(x)= { x+1 xa

Answer 1

what does x</=a mean? this?\[x \le a\]

Answer 2

yes

Answer 3

kk cool. so it seems like all values of a f is continuous from - to + infinity.

Answer 4

Yes

Answer 5

You can plug in any number, therefore it's continuous from - to + infinity for your domain. But for your range, that won't be necessarily true because x^2 will only give you + infinity, since there are no real negative squares.

Answer 6

What am I looking for with this type of problem?

Answer 7

that x has to be equal to a from both ends to make a continuous line?

Answer 8

It will be continuous for all a, won't it? If you started at negative infinity on either one of those graphs, you could draw a line without picking up your pen all the way to positive infinity, couldn't you? (I mean, obviously you couldn't but you know!)

Answer 9

I'm trying to understand. I don't understand anything with math. Looking at this problem, I figured that the answer was already there and I don't understand what needs to be done

Answer 10

If x can equal any negative or positive # + 1, then its already < or = to a

Answer 11

Yeah, it's a weird problem I admit. I wouldn't say you don't understand anything with math though if you picked up that it's already solved. I'd say you know exactly what's going on, it's just an odd question asking a very simple question and you're second guessing yourself, that's all. I mean, there's no dependence on "a" at all, so why did they even bother to say anything? Weird.

Answer 12

I got a medal, not sure what for, but THANKS :D!
Well, with this project, the teacher wants us to write out our reasoning

Answer 13

Well I think the reasoning is all here, just write out what you think and I can check it if you like, and if you feel like it's too obvious or easy, that's probably because it is. =D

Answer 14

but I don't understand what it is that I'm looking for. All I see is that the question is already answered. I do understand that there may be a hole or something, somewhere. Maybe.

Answer 15

Oh there might be, I was looking at the problem all wrong.

Answer 16

OK so basically you're looking for at what point one graph turns into the other graph to keep it continuous, so set the equations equal to each other and solve for x. That x will be the value at which both graphs intersect, so from there you can set your a equal to that one (or two) values to allow the graph to make a complete transition. I'll show you a picture.

Answer 17

So where the two graphs are equal, that's where you want to set your a equal to so that when x=a you have a smooth, continuous transition. Sorry for the confusion, I am drunk.