Question

how do i graph continuity functions?

Answer 1

Use graphs and tables to find the limit and identify any vertical asymptotes of

Answer 2

@Vandreigan

Answer 3

Hmm, so, the way I do these kind may be a little different than how you are used to it, but I'll try to explain as I go.

What happens if we just plug in 5?

Answer 4

I should ask, do you know what the limit of this is?

Answer 5

if you plug in 5 you get 1/0 and that would be 0..... and no i dont .-.

Answer 6

Ok, 1/0 is correct, but it isn't zero. It's undefined.

If we start from 4 and plug in numbers that get closer and closer to 5, what happens? What answers do we get out?

Answer 7

4= 1/-1=-1

Answer 8

Right. What about 4.5? 4.9? 4.99? 4.999? 4.9999?

Answer 9

idk.... how do i plug this into a calc .-.

Answer 10

You can.

The answer is that the answer gets larger and larger and larger, but it's negative.

\[\lim_{x \rightarrow 5^-}\frac{1}{x-5} = -\infty\]

Because we are DIVIDING by x-5, whenever this goes to zero, we have a vertical asymptote there. In this case, we have a vertical asymptote at 5.

With this, can you graph the function?

Answer 11

So, to graph this, we set up with what we know:

You can then just plug in a few values that are less than 5, and plot the result. Then draw the line to connect them.

You can do this for values above 5 as well. But don't use a line to connect points that are on opposite sides of the dotted line (our asymptote)!

Answer 12

do you think you can help me with another one?

Answer 13

I can try :)

Answer 14

oh lol sorry okay soooo Find the indicated limit, if it exists.

Answer 15

Let's do the left-handed limit first. Which part of the function will we use?

Answer 16

the first

Answer 17

Yep :)
So, what's the left handed limit?

Answer 18

Just plug in what the x is approaching in the limit. Is the result undefined? Or does it give you an actual answer? If so, what is that answer?