Help me study?

[brazen dirge]

Can anyone answer my questions about matH

[west ore]

What are you questions? 🤔

[brazen dirge]

wait here

How do you graph rational functions in the form y=a/x-h + k and identify key components

@here

[west ore]

You may be missing parentheses

Did you mean
y = a/(x-h) + k?

[brazen dirge]

yah thats what I mean

sorry

[west ore]

Remember the subtraction would come after the division because of order of operations

[brazen dirge]

ok

I see

[west ore]

Here is a tip that may help:
It is the same as the graph of a/x + k except shift everything to the right by a distance of h.

And a/x + k is the same as a/x except shifted up by a distance of k.

[brazen dirge]

I see

[west ore]

Can you graph a/x?

[brazen dirge]

yes

[west ore]

So you can graph y = a/(x-h) + k?

[brazen dirge]

is it just a horizontal and vertical shift?

of a/x

[west ore]

Yes

[brazen dirge]

I see thanks for explaning

also, how would you find the vertical, horizontal, and slant asymptote from a/(x-h) +k

[west ore]

And in general if you replace x with (x-h) for anything (like x^2 or 1/x whatever) then it would be shifting the graph to the right by a distance of h

[brazen dirge]

I see

[west ore]

Do you know how to find the asymptotes for 1/x?

[brazen dirge]

no

Im sorry if I seem dumb

[west ore]

Okay that’s fine. It just means you haven’t learned it yet

[brazen dirge]

ok thanks!

[west ore]

Do you know what asymptotes are? Like you do know the meaning?

[brazen dirge]

they are areas where the lines get close but never touch

[west ore]

Yes it is something like that except I am not sure if we are thinking of the same thing

[brazen dirge]

can you explain what you're talking about

I think you might be correct

I just have a vague definition

[west ore]

Perhaps just looking at examples would explain it.

Go to desmos and graph 1/x

[brazen dirge]

k I did

[west ore]

If you go down the right side, it gets closer and closer to the line y = 0

[brazen dirge]

right

[west ore]

Which is a horizontal asymptote.

[brazen dirge]

I see

[west ore]

So the horizontal asymptote on the right side is y = 0.

And it is the same on the left side too.

[brazen dirge]

Right

[west ore]

Vertical asymptotes are like the same thing except vertical 😂

[brazen dirge]

lol

funny definition

[west ore]

So if graph x = 0

[brazen dirge]

right

[west ore]

with the y = 1/x too

Then you can kind of see how x=0 is the vertical asymptote

[brazen dirge]

I see your point

cuz the lines never actually touch

but get close

[west ore]

And if you shift the whole graph by h to the right, then vertical asymptotes will shift by h to the right too.

[brazen dirge]

right

[west ore]

And if you shift the whole graph by k upwards, then horizontal asymptotes will be shifted upwards by k too.

So that’s kind of the idea

[brazen dirge]

so y=0 right?

[west ore]

For what?

[brazen dirge]

for the horizontal asymptote

when you shift up

[west ore]

Yes

[brazen dirge]

can you calculate the asymptotes from this question: 2x-3/x+1

[west ore]

If you keep going to the right, will it approach a value, keep going up forever, or keep going down forever?

[brazen dirge]

can you explain how to do algebraically?

[west ore]

Well the thing is

I don’t think there is a horizontal asymptote, so doing algebra won’t help you find it

You were supposed to say it will keep going up forever.

[brazen dirge]

oh is that the case?

[west ore]

Yes

And if you keep going to the left, then it will go down forever.

[brazen dirge]

can you use polynomial divsion to write it in 1/x form

[west ore]

The 2x term will become very large while the 3/x term will become near 0.

[brazen dirge]

oh I see

[west ore]

Oh maybe you forgot to write parentheses?

[brazen dirge]

Here I will send you a screenshot

[west ore]

That would be (2x+3)/(x+1)

[brazen dirge]

oh really?

[west ore]

Yes which is not the same as 2x + 3/x + 1

[brazen dirge]

oh ok Im really sorry

[west ore]

Yeah I guess it could be confusing since they didn’t write parentheses there 😂

[brazen dirge]

oh ok

[west ore]

The difference is that their division has a horizontal bar which sort of has imaginable parentheses around the numerator and denominator

[brazen dirge]

i see

i will remember

[west ore]

But if you just write a / for division then it only divides the stuff right next to it.

[brazen dirge]

i see

[west ore]

So which part are you on? b?

[brazen dirge]

yah

[west ore]

Well what did you get for part a? Maybe those will give you a hint.

[brazen dirge]

I got that the higher the input, the higher the y value

[west ore]

I think you may have typed it into the calculator wrong.

Maybe you forgot the parentheses?

[brazen dirge]

oh we arent allowed to use calculators for this

[west ore]

Oh you are using long division?

[brazen dirge]

polynomial division

[west ore]

So what did you get for a?

It says you were supposed to have 4 decimal places.

[brazen dirge]

our teacher said it doesn't matter as long as we know the end behavior of the graph

[west ore]

So you didn’t do part a?

[brazen dirge]

I did, but I just looked at the pattern

[west ore]

Your pattern was wrong 😔

Should look something like this.

Or if you want to use long division 🤨 I can show you that

They are decreasing each time, but by smaller and smaller amounts so that they approach 2.

[brazen dirge]

Ohhh