Question

Here's a screenshot of a graph and a series of questions relating to limits: http://prntscr.com/151vzw

Any help would be greatly appreciated.

Answer 1

So what have you tried so far?

Answer 2

Oh, and what does x represent? y is clearly cost in dollars, but what is x?

Answer 3

You know it doesn't say....
Huh.

Answer 4

I believe i. is 56 and 2. is 68 but I'm not positive on how to write out how I got there in a way my teacher will understand. -laughs-

Answer 5

And I don't know much beyond that.

Answer 6

Well, it probably isn't distance or the graph would be a smooth line. If I had to guess, I'd say it's some period of time.

Answer 7

I posted the entirety of the problem but... well, it doesn't make much sense, does it?

Answer 8

It seems clear enough. It's asking for the limit from the left and from the right of a certain value (60, in this case) and asking why the function jumps.

Answer 9

Alright, good, someone understands it. -laughs- Would you mind walking me through it?

Answer 10

OK, the limit from the left is the value the function approaches from the left of the graph at that point. You can read that right off of your graph. The right is the same thing, but from the right.

Answer 11

Ok, so i. is the line near the top?

Answer 12

That's (ii). (i) is from the Left (values increasing)

Answer 13

Oh! Alright, I'm following now.

Answer 14

So now you have the first two. The third one is probably because rentals are not on a continuous rate but rather step up on an hourly, daily, weekly, etc. basis.

Answer 15

So the first two are, what? 60 and... 65 maybe? Do I have to format those or show how I got them? What am I suppose to conclude? -laughs- I'm still confused

Answer 16

Looks to me like the first two are clearly indicated on the left (just draw a straight line over from the y-axis)

Answer 17

56 and 68?

Answer 18

Yup!

Answer 19

Alright, I feel smart! -laughs- And the graph is showing the it's not a continual rise of price so much as a jump from price package to price package?

Answer 20

A jump whenever you get into the next time period, rather than a simple "we'll take the time and multiply by some factor" arrangement.

Answer 21

Seems a bit like questions 3 and 4 are sort of the same.

Answer 22

Sorry, I skipped 3 and went to 4. For question 3, because the left and right limits are different there is no single value for the limit overall, so it does not exist.

Answer 23

Ooooh, that's why it jumps, right?

Answer 24

It's actually the other way around. The limit does not exist *because* the graph has a discontinuity (a "jump" rather than a "kink", in this case).

Answer 25

Oh! Well that makes sense. I think I've figured it all out now! Thanks! You were a big help!