precalculus

[viscid thistle]

so it's done?

[rapid lance]

yes it is

[viscid thistle]

cool

[rapid lance]

initially i had 12^4 as -1

thats what messed me up

[viscid thistle]

lol, it's a lot of arithmetic bashing

[rapid lance]

yes it is, i wish i had a calculator with me rn :V

now my question is, is there an easier way to prove something like this?

[viscid thistle]

probably not

in fact, many problems like this, where the variables are in the third, fourth, or higher degree are extremely hard

[rapid lance]

yea, i had a few earlier with second powers and third power, i just used elliptic curves, but this one didnt work for that

[viscid thistle]

you are in 8th grade and using elliptic curves on diophantine equations?

[rapid lance]

yea

[viscid thistle]

rip my self esteem

[rapid lance]

lol

[viscid thistle]

there are a couple good diophantine problems in the #challenge-problems channel if you want some more problems like this

although they are finding solutions, not proving that none exist

[rapid lance]

thanks, i find dinding solution is easier, i will them out 🙂

[viscid thistle]

lotto advanced people here

[queen forum]

f(x)=1/sqrt(x-9) Is there a method to find the range of this function algebraically?

[weak needle]

Yeah

Get the values that function will never produce

Then remove those from the real numbers

[mighty stump]

Help with this

I don’t know where to start

[weak needle]

Help with this
@mighty stump Let me check

[queen forum]

Thanks^

[weak needle]

@mighty stump You have the y coordinate. The radius is your hypotenuse

Work from there

[mighty stump]

where would i place the triangle

[weak needle]

You don't need to place it

Just remember the Pythagorean theorem

@mighty stump Did you get it?

[mighty stump]

no

i just dont understand how to use everything given

[weak needle]

Alright

Let's do it together

What does 4/5 mean in your problem?

[mighty stump]

y of P

[weak needle]

y is a distance

From where to where?

[mighty stump]

from P to the origin?

center

[weak needle]

from P to the origin?
@mighty stump From P to the x-axis

[mighty stump]

oh

[weak needle]

What's a radius?

[mighty stump]

oh and then 1

ok

[weak needle]

You got it

[mighty stump]

3/5

[weak needle]

What's 3/5?

[mighty stump]

side of triangle from P

[weak needle]

3/5 is the distance of P from the y axis

[mighty stump]

yea

[weak needle]

Or x

So P=(-3/5, 4/5)

Remember that x=-3.5 because it's in the second quadrant

[mighty stump]

yep

[weak needle]

Then finding the trigonometric ratios is simple

[mighty stump]

so i create a triangle from the given points,

and then just use sohcahtoa

[weak needle]

yes

Pretty much

[mighty stump]

thanks

so much

[weak needle]

You're welcome!!

[mighty stump]

would the distance between P and (1,0) be 1.788854?

[weak needle]

would the distance between P and (1,0) be 1.788854?
@mighty stump Why do you need that?

[mighty stump]

to create a triangle from P , (1,0) and center

i wasn’t supposed to do that was I

[weak needle]

Wait a sec

[mighty stump]

yeah

i got that part

[weak needle]

Then why do you need (1,0)

?

[mighty stump]

to find trig t

[weak needle]

No you don't need it

[mighty stump]

but then how do i find sin t and such

[weak needle]

What's the definition of sine?

[mighty stump]

opposite/ hypotenuse

[weak needle]

y/h

[mighty stump]

what?

i dont understand what you mean by y/h

[weak needle]

i dont understand what you mean by y/h
I meant y/r

Read the second page of this:
https://www.math.utah.edu/lectures/math1060/1-4PostNotes.pdf

[mighty stump]

i see

sin = -3/5 / 1

or no i would have to place x and y into that equation to get r

[eager path]

why is the sum of odd entries in an even row of pascal's trinagle equal to the sum of even entries in the same even row?

[mighty stump]

meaning 1

[eager path]

https://gyazo.com/62844cf424fbd06b76ed40a1bc37e180 for example, in the fourth row

1 + 6 + 1 = 4 + 4

{the odd entries sum} = {even entries sum}

why is that?

[weak needle]

or no i would have to place x and y into that equation to get r
@mighty stump You already have x, y and r

[mighty stump]

yea i realized that

[weak needle]

https://gyazo.com/62844cf424fbd06b76ed40a1bc37e180 for example, in the fourth row
@eager path Ugh, combinatorics...

[mighty stump]

that means sin is 4/5, cos is -3/5 and cos is -4/3 ?

[weak needle]

that means sin is 4/5, cos is -3/5 and cos is -4/3 ?
@mighty stump Why do you get different values for cos?

[mighty stump]

meant tan

for last

[weak needle]

Yeah

[mighty stump]

would cos 2t just be -6/5

[weak needle]

would cos 2t just be -6/5
@mighty stump No

Look for something called sum of angles identity for sine. Double angle identity for sine will get you straight to the point.

[simple edge]

what are the steps to prove this has no limit

[viscid thistle]

@simple edge what have you tried

Also "this has no limit" is vague, use "this limit does not exist" on any case

[simple edge]

multiplying top and bottom by 1+cosx

ok

[viscid thistle]

So what you can do is to evaluate this limit from both sides, and if they are not equivalent, the limit does not exist.

@simple edge

[simple edge]

ok

@viscid thistle do i use close values to 0 to get approximation

nvm i see it

thx

[viscid thistle]

Yeah

Np

[wide rampart]

What happened here?

[icy ingot]

-ln(1/2) is the same as lin(1/2)^-1 so it just reciprocated to (2/1)^1 which is just 2

[viscid thistle]

If somone has some time could y’all let me know if I use union or 2 different interval notations to show the line between 3-4 please and Thankyou.

[-3,4] is fine

[icy ingot]

Thats what I was thinking for the range

Domain*

[viscid thistle]

you could say [-3,3) ∪ [3,4] but there is no reason to do that

Oh okay Thankyou, I was thinking I maybe needed separate ones,thanks again

[fleet yew]

nice

[violet knoll]

Need help on the first step. Thanks!

[icy ingot]

x= square root of 5y-25. The domain of f is [5,infinity) so the range of f^-1 would be [5,infinity)

Solve x from there

So to find the domain of f^-1, find the range of f

[novel cargo]

I'm not sure where to put the vertex considering that focus is center of earth

[harsh smelt]

any of poles for example

i guess

[novel cargo]

is this for convenience that we choose to do so?

Or are we constrained to do this?

[harsh smelt]

well it is natural

you can put vertex to sun if you want lol

[novel cargo]

oh, so physics

[slow roost]

how come sec 29pi/4 is -sqrt2

not sqrt2

ik i have to subtract it by 2pi

but i remember theres a faster approach where i choose a number closest to 29 but when i divide, it comes back as 2

if i continously subtract 2pi, then im able to get 5pi/4

which is what gives me te right answer

so ultimately its subtracting 6pis from it

[slow roost]

<@&286206848099549185>

[harsh smelt]

29pi/4 = 7pi+pi/4

@slow roost where is 7pi + pi/4?

[slow roost]

o.

3rd quadrant

wai why 7pi

bc 7*4=28

and thats the closest to 29?

[harsh smelt]

yes

and also

if i continously subtract 2pi, then im able to get 5pi/4
this is equvi

[slow roost]

yeah

but i feel like its more time consuming

ooo

and since its 7pi

that isnt divisible by 2

hence why u add another pi/4

ooooo

@harsh smelt

is that the right way to think about it

[harsh smelt]

29pi/4 = (28+1)pi/4

any further clarifications needed?

also you could do it as
29pi/4 = (32-3)pi/4 = 8pi - 3pi/4 and get equiv answer

anyway the task was to make it proper fraction and to get info about how many rotations were produced

[slow roost]

yeah

alright ty!!!

[novel cargo]

are the asymptotes of a hyperbola the same intersecting lines that occur if we cut a double cone with a plane exactly in half?

[willow bear]

"exactly in half" is vague

[novel cargo]

a plane that cuts through the vertex of the cone and is paralel to the cone axis

[willow bear]

so a plane that just goes through the cone axis

then yes

[novel cargo]

good thing is that you also teach me how to talk precisely like a mathematician

double thanks

$\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1$

[obsidian monolith]

az:

[novel cargo]

when the y^2 term is negative the transverse axis in horizontal and vice versa

I can't wrap my head around this

can't reason about this

[turbid violet]

Any help on how left side can be simplified to right side would be greatly appreciated. Tried e^ix = cos(X) + isin(X) but it isn't working out

[novel cargo]

$\abs{\frac{ie^{-w_{0}\frac{t}{2}} - e^{iw_{0}\frac{t}{2}}}{2\sqrt{2}}}^2 = \frac{1 - \sin{wt}}{4}$

[obsidian monolith]

az:

[viscid thistle]

If you multiply LHS by i/i you get the complex sin

[turbid violet]

I'm not given the right hand side, I'm just given the left and need to somehow change it into the RHS

but according to my prof solutions, that's what I'm meant to get, but he doesn't show how and I can't work out the process

[viscid thistle]

I meant to say LHS

My bad

[turbid violet]

np np, let me try that out, thanks mate

[viscid thistle]

If you multiply LHS by i/i you get the complex sin
Inside the abs of course

[proud crypt]

@patent beacon sry for ping

but can we do our derivatives stuff agian

so if i have

$ ax^n $

argh texit difficult

anyway

a x^n

what would the derivative be

[obsidian monolith]

Josiah Mo:

[proud crypt]

the formula

oh late response

texit is lagging lo

[viscid thistle]

$(3x{\color{green}{³}})'={\color{green}{3}}\cdot 3x^{3-1}=9x^2$

[obsidian monolith]

Al𝟛dium:

[viscid thistle]

I can give you a general formula if you want

[proud crypt]

ok yes

(im going into 8th grade dont use too advanced words lol)

and im only going into alg 2

just got curious 2 day sago

so if it involves something advanced

oh

off

[viscid thistle]

$(ax^n)'=a\cdot nx^{n-1}$

[proud crypt]

ummm

[obsidian monolith]

Al𝟛dium:

[viscid thistle]

What?

Is this adv for you?

[proud crypt]

i dont get it

well no

but teh formula is confusing

[viscid thistle]

Okay

Let me clarify, did you understood the example i gave above?

[proud crypt]

can u give like an example

i tink

[viscid thistle]

Another example if you want

[proud crypt]

yeah

with steps

im doing alg 2 in 8th grade this fall

but i got curious with what a derivative was

so i kinda went ahead

evne tho i only know 50 percent o

ff alg 2

[viscid thistle]

$({\color{blue}{7}}x^{\color{green}{5}})'={\color{green}{5}}\cdot {\color{blue}{7}}x^{{\color{green}{5}}-1}=35x^4$

[obsidian monolith]

Al𝟛dium:

[viscid thistle]

Hope the colouring makes it clearer

im doing alg 2 in 8th grade this fall
We get it you don't have to repeat it every minute

Lol

@proud crypt look at the new example

[proud crypt]

ok

oh the coloring is better thx

gosh u are good with texit

@viscid thistle oops sry ig i got carried away

[viscid thistle]

Thanks lol

[proud crypt]

so...

$ax^n$

[obsidian monolith]

Josiah Mo:

[viscid thistle]

Don't worry :)

[proud crypt]

lol

yeah pride is an issue with me ig

[viscid thistle]

Let me see if the formula clarifies with this wait a sec

[proud crypt]

also comparing myself to others lol

like "oh everyone else is doing topology im dumb"

ok s

O

the derivative of ax^n

would be

exponent mutlipled by current coefficient

making new coefficient

exponent - 1

[viscid thistle]

$$({\color{blue}{a}}x^{\color{green}{n}})'={\color{green}{n}}\cdot {\color{blue}{a}}x^{{\color{green}{n}}-1}$$ $$({\color{blue}{7}}x^{\color{green}{5}})'={\color{green}{5}}\cdot {\color{blue}{7}}x^{{\color{green}{5}}-1}=35x^4$$

also $(c\cdot f(x) )'=c\cdot f' (x) $

[proud crypt]

so...

[obsidian monolith]

HoboSas:

[proud crypt]

is my interprtation correct?

[obsidian monolith]

Al𝟛dium:

[proud crypt]

coefficient gets multipled by a factor of the exponent

exponent minus 1

[viscid thistle]

Yes

I'd say

1. Bring down coefficient as an factor
2. Substract 1 to the exponent

But yes

[proud crypt]

ok

but why does this work

ik how to use a basic derivative i think

so if we have $ y = x^2$

[obsidian monolith]

Josiah Mo:

[proud crypt]

and we also have $ y' = 2x'$

[obsidian monolith]

Josiah Mo:

[viscid thistle]

but why does this work
You would have to use the definition of derivative, which involves limits

[proud crypt]

oh

[viscid thistle]

Without the ' on the 2x

[proud crypt]

oh oops

well lets say u haev x = 3

x: 3
y: 9
slope: 6

awesome the possiblities for this seem endless

one question tho

how can a singular point have slope

[viscid thistle]

Singular?

It can't...?

What?

[proud crypt]

wait so the slope of the line

at x = 3

is 9 righ t

according to a derivative

but wait

isnt (3, 9) a point not a line segment or cuve/

[viscid thistle]

Derivative is a tool to locally approximate functions as lines

(3, 9) can represent a vector too

is 9 righ t
It's 6

[proud crypt]

oh right

well y = 9

slope = 6

wait

Derivative is a tool to locally approximate functions as lines
@viscid thistle huh??

[viscid thistle]

Try to draw it

[proud crypt]

ok

wait how

can someone do it for me or teach me how to use texit

[viscid thistle]

Try to draw it
On paper

[proud crypt]

oh

ummm

howbout wolfram alpha

or desmos

[viscid thistle]

Come on

Don't be lazy

[proud crypt]

why

does it benefit me to draw on paper

[viscid thistle]

line is y=6x-9

[proud crypt]

wait wut

isnt it y = x^2

[viscid thistle]

Exercise

[proud crypt]

and 2x

oh ok

lemme see if i ran out of graph paper

[viscid thistle]

||,w plot *function*||

But yeah practice

[proud crypt]

ok

[viscid thistle]

line is y=6x-9
This is the tangent to x^2 when x=3

[proud crypt]

equation: y = x^2
derivative: y = 2x

right

[viscid thistle]

Yes

[proud crypt]

ok

wait one problem

[viscid thistle]

Would add y'

[proud crypt]

im on pc

so i cant take pics

[viscid thistle]

Then use desmos ig

[proud crypt]

ok

oh oops

it was 2x not 2x-1

wait a sec

2x-1 seems right

huh??

[viscid thistle]

2x-1 is tangent when x=1

[proud crypt]

yes...

so which one is the derivative

[viscid thistle]

-1 only moves the actual function

[proud crypt]

oh

stupid me

ahh yes

ok so my point is

So derivatives:

take a point and plug in

but points cant have slopes

only lines can

[viscid thistle]

I mean 2 points can give us a slope not 1: $m=\frac{y_2-y_1}{x_2-x_1}$

[obsidian monolith]

Al𝟛dium:

[viscid thistle]

Because those 2 points can form a line

[proud crypt]

ok sry im so dumb but still confused

a derivative finds the slope of a point right

[viscid thistle]

Of a point

Remember what we said above

[proud crypt]

but derivative doesnt use 2 points

right?

from what i can tell it takes 1 point as input

and returns slope

i never see 2 points

[viscid thistle]

The derivative of a function or the equation of a line

[proud crypt]

huh sry me still confused

im dumb

wait so what does a derivative do

[viscid thistle]

Don't worry about it, you are learning adv stuff if you are on 7/8th grade

Derivative is a tool to locally approximate functions as lines
Here

[patent beacon]

Okay, so do you know what a tangent line to a function is? @proud crypt

[viscid thistle]

He is about to do 8th grade lol

[patent beacon]

Up to you if you do want to know Josiah, you will, probably soon, have more experience and the opportunity to learn this

[viscid thistle]

The derivative  is a way to show rate of change, which is the amount by which a function is changing at one given point.

If you want a more formal definition

@proud crypt you there?

[patent beacon]

I do suggest 3b1b's essence of calculus series, if you want to get more grasp on this

[proud crypt]

oh yeah sry i had to do smth quickly

@patent beacon i think so?
like the line that touches the function

at the bottom i think

once

like tangent to circle

but how can a derivative

show rate of change

if it takes 1 point as input?

like if u have

[patent beacon]

Yeah yeah, it's a line that just touches the function.

Let's say you pick a point on the function at x. Then construct the tangent line there. The derivative gives you that line's slope

[proud crypt]

ok

$ y = x^2 $

[obsidian monolith]

Josiah Mo:

[proud crypt]

and

[viscid thistle]

if it takes 1 point as input?
no it does not

[proud crypt]

$ y = 2x$

[obsidian monolith]

Josiah Mo:

[patent beacon]

We cheat a little bit and just say that this is "the slope of the function at that point"

[proud crypt]

so if u have x value 3

x: 3
y: 3^2 = 9
slope: 6

im correct so far right

[patent beacon]

Yaya

[proud crypt]

so the thingy is taking (3, 9) as its input

right?

[patent beacon]

It's also taking the function y = x² as an input

[viscid thistle]

^

[patent beacon]

Mind you, we didn't talk about how we actually determine what derivatives are, but you do need to feed the function in to get the derivative info

[proud crypt]

oh

so the function is also an input

gosh me is dumb

[crystal osprey]

That's essentially what functions are. They show the relation between an input and an output.

Also, it's usually nice to know the context of a function to dissect its information easier.

[grim sand]

What is domain and range

😔

[willow bear]

the domain of a function is the set of inputs you can plug in without there being a calculation error (division by zero, root of a negative number, or log of a non-positive number)
the range is the set of all outputs your function produces

[rapid tangle]

How do i solve this? Either using trigo or differntiation

[willow bear]

complex numbers allowed?

[peak badge]

Yeah, I think I derived this result using De Movire's Theorem/Euler's Form.

[willow bear]

i am asking codin if that's a route they are allowed to take

[peak badge]

I know.

[willow bear]

@rapid tangle?

[rapid tangle]

@willow bear no complex numbers not allowed because they haven't taught us that yet....it would be nice if only trigonometry is used

[willow bear]

welp lmao

uhh

lemme see if i can come up with sth

[grim sand]

the domain of a function is the set of inputs you can plug in without there being a calculation error (division by zero, root of a negative number, or log of a non-positive number)
the range is the set of all outputs your function produces
@willow bear too many big words for me

😔💔

[willow bear]

what big words

[grim sand]

Everything

[willow bear]

i specifically tried to make it so that there were not that many big words

[grim sand]

May b I jus slow

😔💔

[willow bear]

bruh

[rapid tangle]

And could this also be solved using differntiation too? not that I'm allowed to do that...just for curiousity's sake @willow bear

[willow bear]

the more vague you are in stating your doubts, the less i can help you @grim sand

[grim sand]

I’m sorry sir/ma’am

I’m bout to take a test on domain and range

And I don’t know what it is

😔💔

[willow bear]

about to take a test?

well then you're kinda fucked i guess because no amount of explanation will fix the hole in your knowledge THAT fast

[grim sand]

Yessir

Just got a 3/10

It was due in 30 mins 😔

[viscid thistle]

[grim sand]

It’s online

And I couldn’t even cheat

Cuz I didn’t know what to search

[willow bear]

don't sir me

if you insist on using an honorific and not just my name then please use ma'am

@rapid tangle yeah so it turns out there is a purely trigonometric way to do this

[grim sand]

I use yessir for everyone 😔💔

I use sir/ma’am the first time

[willow bear]

ok i specifically am asking you not to call me sir because i really fucking don't like being called sir

[grim sand]

Ok

Tone the language down tho ma’am

[willow bear]

that is already toned down

[viscid thistle]

how can you be about to take a test which you got a 3/10 on, and was due in 30 mins

[willow bear]

@viscid thistle time travel

[rapid tangle]

@willow bear how

[grim sand]

how can you be about to take a test which you got a 3/10 on, and was due in 30 mins
@viscid thistle due in 30 mins

Finished in 1 min

[willow bear]

@rapid tangle are you ok with sigma notation?

[grim sand]

are people so lazy that they can't even get a decent picture for people they want homework from?
@Fiwam#4468 yes

Oh he left

[rapid tangle]

@willow bear yes

[willow bear]

okay great

so the thing to pull out of your ass here is multiplication and division by sin(θ/2)

[rapid tangle]

Wait what

[willow bear]

here lemme show you

[rapid tangle]

Yess

[willow bear]

excuse my bad handwriting

[rapid tangle]

No that's fine and what u did there is big brain but what's a telescoping sum tho

[willow bear]

ok so basically if you write it all out

the cos(3/2 theta), cos(5/2 theta), cos(7/2 theta) etc terms will cancel out

the ones in the middle will

the only thing that's left is at the ends

more generally $\sum_{k=1}^n (a_{k-1} - a_k) = a_0 - a_n$

[obsidian monolith]

Ann:

[rapid tangle]

Ohhhh i get it damn this is such an elegant solution

[willow bear]

it's big brain

[rapid tangle]

Big pp

Thanks tho

[novel cargo]

is y = k/x a hyperbola?

[heady lotus]

Yes, any equation of the form xy = k is a hyperbola

[novel cargo]

how can we show that by converting y = k/x to the standard form x^2/a^2 - y^2/b^2 = 1 ?

[heady lotus]

We have y = k/x
So we get xy = k
Now define a new coordinate axes with X axis and Y axis where X = (x + y)/2 and Y = (x - y)/2
Substituting in xy = k, we get,
(X +Y)(X - Y) = k
Which gives X^2 - Y^2 = k

We define the new coordinate axes like that because xy = k is basically a rotation of 45 degrees of the hyperbola x^2 - y^2 = 1 about the coordinate axes

[novel cargo]

wow

this is cool

thank you

I think that's gonna come up later in my precalc book

rotation

also, the asymptotes are the original axis

[heady lotus]

No problem ✌

Yes

[proud crypt]

ok so heres what ik about derivatives so far:

1. what it is

2.the proof of how ti works

3.the general formula

but how do i do it if i have a polynomila?

like $ x^2 + 5x + 4$?

[obsidian monolith]

Josiah Mo:

[proud crypt]

im preety sure u have to use dy/dx on everything but not sure...

[blissful ridge]

What is that you wanna do?

[proud crypt]

turn the polynomial in ao a derivative

well find its derivative

i only know so far how to do with monomials

[harsh smelt]

derivative is linear

[proud crypt]

yes...

[willow bear]

parentheses

[obsidian monolith]

Commander Vimes:

[proud crypt]

oh i think i see

take the derivative of every term in teh polynomial

[harsh smelt]

since polynomial is just linear combination of monomial it follows

ye

[proud crypt]

like distributive property

cuz ist monomials put together

awesome

lemme try one

altho i suck with texit

ill just not use texit actually

so if we have

$ x^2 + 5x +4 $

[obsidian monolith]

Josiah Mo:

[proud crypt]

derivative would be

wait lemme try with texit

derivative would be $2x + 6$

[obsidian monolith]

Josiah Mo:

[proud crypt]

am i right?

[willow bear]

no

2x+5

[proud crypt]

huh

[willow bear]

the derivative of 5x is 5

[proud crypt]

but wiat

[willow bear]

the derivative of 4 is 0

[proud crypt]

so its $ 5x^1$

[obsidian monolith]

Josiah Mo:

[proud crypt]

o0h ok

5 * 1 = 5

and 4 would be

wait

0?

so 4 = 1 * 4^1

wouldnt derivative of 4 be 1

cuz exponent - 1

is 0

4^0 = 1

*1 = 1

so its 1?

[uncut mulch]

no

$4 = 4x^0$

[obsidian monolith]

ramonov:

[proud crypt]

ohhh

so its not 1 * 4

its 4x^0

so its 0

[uncut mulch]

i mean its both

[proud crypt]

cuz itd be

0 * 1/4

so its 0

both?

howcome mine doesnt work

[uncut mulch]

because you're trying to forcibly use a rule where it doesn't apply

[proud crypt]

oh ok

[uncut mulch]

4 = 1*4^1 is true. however the power rule doesn't apply as 4^1 doesn't have a base of *x

[willow bear]

4 is a constant

[proud crypt]

ahh i see i think

[grim sand]

Can someone help me so how would I find domain and range of this.

Would range be infinite? Or would it stop at 3

[novel cargo]

the range is the output of a function or what you can see on the y axis

looking at the graph, what range of the y axis does it cover?

[grim sand]

Basically it doesn’t stop

The Y just keeps going

So it would be INF right

[novel cargo]

the y goes up but does the graph goes above 3 on the y axis?

[grim sand]

No the Y stays at 3

Oh

(-INF,3)

Yes

[novel cargo]

(-inf, 3]

[grim sand]

Thx

Yeah

[novel cargo]

3 is closed

[grim sand]

So if it’s closed it would be ] instead did )?

I never understood the difference in those

[novel cargo]

it's closed when the point itself is also included in the interval

[grim sand]

Oh okay

[novel cargo]

the graph can never hit inf itself

bit it hits 3

[grim sand]

How do I find domain of this I only know how to do the graph ones

Since domain is all X

What is X since it’s Y=

[novel cargo]

is domain the whole R?

aren't there exceptions?

[grim sand]

What’s exceptions

Would I need to graph this myself

[novel cargo]

aren't there any values in R that you can't substitute for x because it won't make any sense?

[grim sand]

No..?

Where’s r

[novel cargo]

real numbers

[grim sand]

I don’t think so

That’s all it’s giving me

[novel cargo]

what about 0?

[grim sand]

Vertical asymptote would be 0

[novel cargo]

so you saying we can divide 2 by 0?

[grim sand]

This would be the graph

Ummm no

I’m lost

I only know how to do the simple graphs 😔

[novel cargo]

does the graph ever reach 0 on the x axis?

think about it this way

[grim sand]

Teacher told me it never touches 0

[novel cargo]

you see

[grim sand]

On these type of graphs

[uncut mulch]

2/0 is undefined hence 0 is not part of the domain

[novel cargo]

^

[grim sand]

So how do I find the domain..

[novel cargo]

you can put any number for x except for 0

that's the domain

[grim sand]

So INF

[novel cargo]

how do you express this?

NO

[grim sand]

-INF

[novel cargo]

the domain is one or more interval(s) of numbers

inf doesn't make sense

[grim sand]

Can u give me an example

[novel cargo]

(-inf, 0), (0, inf)

interval is open at 0, so 0 is not included

[grim sand]

I’m sorry I’m still lost 😔

[novel cargo]

how would you define the domain

in your words

[grim sand]

All values of X

[novel cargo]

but your teacher said the graph never touches 0

how is it all values of X?

[grim sand]

I think he meant it for the Fim or Lim(x) equations

[novel cargo]

dividing by 0 is not defined

you must always make sure to avoid it

when you have an equation of the form k/x

you must define the domain in way that it excludes 0

[grim sand]

So how do I even find the x values of Y=2/x

[uncut mulch]

its defined everywhere except for 0

[grim sand]

So I can just put any number

[uncut mulch]

the domain is the set of valid inputs

[grim sand]

I’m so lost

[uncut mulch]

do you understand that 2/x is undefined when x=0?
(hence 0 is not part of the domain)

[grim sand]

Yes because 2 can’t be divided by 0

[uncut mulch]

ok good.

[grim sand]

And in the graph X never touched 0 yes?

Touches

[uncut mulch]

weird wording

[grim sand]

But correct?

[uncut mulch]

x doesn't really "touch" values

y is undefined at x=0, there is no corresponding y value at x=0.

[grim sand]

Wait so how do I find a domain

Don’t I just write all the X values

[uncut mulch]

...

[grim sand]

I haven’t had math in 2 years I’m so lost

[uncut mulch]

do i really have to repeat:

do you understand that 2/x is undefined when x=0?
(hence 0 is not part of the domain)

your domain would be all the set of all real values excluding 0

[grim sand]

Because x and Y never touch at 0

Gotta find one where they touch?

[uncut mulch]

which could be represented in interval notation as
(-inf,0)U(0,inf)

[grim sand]

I said INF earlier

But as said no

👁👄👁

[uncut mulch]

because inf by itself does not represent a set of values

[grim sand]

So the domain would be -INF,0

Because x can be any number

At all

Then 0,INF because

I don’t know that one

[uncut mulch]

parentheses

[grim sand]

(-INF, 0)

Wait why isn’t ] there

Doesn’t it stop at 0?

[uncut mulch]

because you're excluding 0

parentheses (or reverse bracket) exclude
bracket include

[grim sand]

Oh

Oh

Excluding 0 so we use parenthesis

[novel cargo]

]-inf, 0[ same as (-inf, 0) then, Ramonov?

[grim sand]

^ I was thinking the same

[uncut mulch]

yeh

[grim sand]

Why use it on INF

R we excluding INF

[uncut mulch]

inf is not a number

[novel cargo]

now, can you ever reach inf?

[grim sand]

So it can’t have a bracket

now, can you ever reach inf?
@novel cargo no?

[novel cargo]

hence the parantheses instead of brackets

[uncut mulch]

if the notation is taught, reverse brackets are less ambiguous than parentheses as those could be misinterpreted as points

[grim sand]

Oh

You guys are smart

Or girls

[undone pawn]

i wasnt taught the rev bracket though

[grim sand]

I can’t assume

i wasnt taught the rev bracket though
@undone pawn me too

[undone pawn]

only heard of it from this server lol

[uncut mulch]

yeh me neither

[grim sand]

You humans are smart

only heard of it from this server lol
@undone pawn me too

[uncut mulch]

i was angry at first but i'm starting to like them

[undone pawn]

lol

yeah theyre not too bad

[grim sand]

I understood the first part now

(-INF,0)

But what about the (0,INF)

Why is it flipped

N what does the U mean

[uncut mulch]

union

[undone pawn]

U is a set union

[grim sand]

What does union do

Or mean

[uncut mulch]

(-inf,0)U(0,inf) would be the combined set of negative and positive numbers,
i.e. the set of real numbers excluding 0

[grim sand]

It’s my 2nd day in online pre calc and my teacher not explaining clearly

I’m having a rough time

Plz help

[undone pawn]

${1,2,3} \cup {6,7,8} = {1,2,3,6,7,8}$

no latex?

😦

[grim sand]

What’s that

[undone pawn]

oh thats great

[uncut mulch]

lol

[grim sand]

I don’t understand that

[uncut mulch]

you need \{

[undone pawn]

${1,2,3} \cup {6,7,8} = {1,2,3,6,7,8}$

[uncut mulch]

or something

[undone pawn]

yeah forgot its a special one

man the latex bot is sluggish today

[grim sand]

Wha.... I can’t even do y=2/x correctly and now there’s...

[obsidian monolith]

FlynnXD:

[novel cargo]

take a deep breath Jupiter

it gonna work out

[undone pawn]

thats what a set union does^

results in a set with both sets' elements

[uncut mulch]

which part are you unsure about atm?

[undone pawn]

well, no repetitions though

[grim sand]

FlynnXD:
@obsidian monolith so it’s just another way to combine them?

which part are you unsure about atm?
@uncut mulch everything

I have no clue what’s going on I only remember my multiplication addition subtraction and division

[undone pawn]

so it’s just another way to combine them?
its another operation between sets

[uncut mulch]

(-inf,0) only represents the negative numbers

[undone pawn]

^

[uncut mulch]

do you understand that?

[undone pawn]

are you familiar with these set notations firstly

[near monolith]

Jupiter, they don't want you to think infinity is a number, and they don't want you thinking $\sqrt{-1}$ is one either

[obsidian monolith]

KD:

[grim sand]

So INF isnt a number

It’s just there

For a x value

[near monolith]

So they want you looking for $\sqrt{2x-1} = \sqrt{-1}$

[novel cargo]

inf is a state of mind

[undone pawn]

$x \in (-\infty, 0) \ \text{is equivalent to saying} \ x< 0$

[near monolith]

You've got to search for those undocumented math entities

Not in MY domain

[uncut mulch]

inf is something used to represent something boundless or something like that

[grim sand]

This is me rn 👁👄👁

I don’t understand math language I’m trying my best to understand

[undone pawn]

give specifics

what exactly is not being understood

[near monolith]

When TeXit renders, it will be more clear

[undone pawn]

and why

lol

[grim sand]

What is $x/in

I’ve never seen those before

[undone pawn]

yeah dont read those

its for the bot

which seems to be lagging a lot today

[grim sand]

Dah bot is gone

So on this how do I do this

The first one I understood now because

0 can’t be used

So exclude 0

And INF can’t be reached

So exclude that

But the graph keep going so it is INF

[novel cargo]

you are dealing with radical in denominator

so, it can't be negative and also not zero

[grim sand]

So (-INF,0) U (connect it) (0,INF)

[viscid thistle]

Is this a test Jupiter

[grim sand]

No it’s some class work

That I have no clue on

N teacher isn’t available till Monday

😔💔

[viscid thistle]

Okay so what's the question

[near monolith]

It's time to use the brain. We hate to do it, but there's no other way

[novel cargo]

you must see for what values 2x -1 <= 0 and exclude them

[viscid thistle]

7 or 8?

[grim sand]

Huh

Where did u find 7 and 8

I’m so lost

[viscid thistle]

The problem 7 or 8

[grim sand]

Oh

Both actually

I have no clue what to do in those

I’m learning step by step from y’all

[viscid thistle]

Okay

[grim sand]

And I thank y’all for your patience

It’s like 4 different ppl helping me and probably raging cuz I have no clue what’s going on

[viscid thistle]

You know what a fraction can't have in the denominator?

[undone pawn]

im raging at the stupid texit bot

[heady mica]

When doing combinations of it’s like g(h(f(x))) can you work from the inside out. So like do h(f(x)) plus all the f(x) function into the x spots in h and then take that function and plus it into all the x’s Of g?

I’m trying to create a 10 function combination and just want to make sure working from the inside out is best

[undone pawn]

@heady mica there is a discussion going on here

[novel cargo]

don't worry Jupiter, the people on this server got you mate

[viscid thistle]

When doing combinations of it’s like g(h(f(x))) can you work from the inside out. So like do h(f(x)) plus all the f(x) function into the x spots in h and then take that function and plus it into all the x’s Of g?

I’m trying to create a 10 function combination and just want to make sure working from the inside out is best
@heady mica occupied channel, move.

[grim sand]

don't worry Jupiter, the people on this server got you mate
@novel cargo thank you

[viscid thistle]

You know what a fraction can't have in the denominator?
@grim sand

[grim sand]

It’s my senior year and for some reason I have such hard classes

So I’m trying my best

@grim sand
@viscid thistle a 0?

[viscid thistle]

Good

[grim sand]

Then what’s next

[viscid thistle]

And what numbers a square root can't take? Or don't have a real solution for them

[grim sand]

Odd numbers

[viscid thistle]

Not exactly

$\sqrt{-3}$ do you think this has a solution over the reals?

[obsidian monolith]

Al𝟛dium:

[grim sand]

No it’s negative

So all negative numbers

[viscid thistle]

Yes

[grim sand]

😃I’m learning

[viscid thistle]

So we don't want 0's and negative numbers on the denominator, do you agree?

[grim sand]

Yes because they don’t work

Just makes the equation have error

[viscid thistle]

Sure so what we usually can do to check for the values of x that can be on the domain for a sqrt in the denominator is to solve for: 2x-1>0

[grim sand]

Huh

[viscid thistle]

Okay

Do you not understand why?

[grim sand]

How do we check for it

For x

And what is 2x-1>0

[viscid thistle]

It's an inequality

You can solve for x

Haven't you seen those?

[grim sand]

No

Want me to send u the earlier ones?

[viscid thistle]

No it's okay

[grim sand]

It has all the stuff we learned in 2 days

Question 1-5 I think I understood

But y’all helped me with 6-8 cuz I have no clue what those are

[viscid thistle]

I may post a youtube video to get you started on inequalities, hold up. They are very simple

[grim sand]

Yes please

[viscid thistle]

https://youtu.be/tm49BYGw_Sg

The beginning of the video is very important for the introductory of inequalities

[rose trellis]

Is this where like questions about ap stats go

[viscid thistle]

If it's stats you can go #probability-statistics i guess @rose trellis

Or any of the #question channels

[grim sand]

We’re not learning this rn

But I’ll watch it

Brb*

[viscid thistle]

Watch the first 10 minutes

The rest is other stuff

[uncut mulch]

solving linear inequalities should definitely come before functions

[viscid thistle]

Indeed

[uncut mulch]

as well as interval notation (conveniently shown above)

[grim sand]

I watched

I understood all of 10 mins

I’m a visual learner so it was so simple watching him do it

@viscid thistle now what

[viscid thistle]

Good

So back to our inequality: 2x-1>0, what do you think the first step is?

[grim sand]

Get X by itself

+1

Divide by 2

[viscid thistle]

Okay yes

[grim sand]

X>0/1

2

X>0/2

I mean

1/2

And it’ll be a open circle

So it’ll be a parenthesis

[viscid thistle]

$2x-1>0\implies 2x>1\implies x>\frac12$ yes

[obsidian monolith]

Al𝟛dium:

[grim sand]

So (-INF, 1/2)

[viscid thistle]

Almost

Look at the >, what do you think it means

[grim sand]

Oh flipped

(1/2,INF)

[viscid thistle]

() but yes

The website is wrong

[grim sand]

Huh

[viscid thistle]

They have [1/2, inf)

Clearly 1/2 is not on the domain

[grim sand]

What equation is that

I thought u just gave me a random one

[viscid thistle]

What?

[1/2, inf) is not an eqn

[grim sand]

U were helping me with question 7?

[viscid thistle]

Yes

[grim sand]

Oh

[viscid thistle]

Lmao

[grim sand]

I thought u just gave me a random one

How’d u simplify the equation to make it look so easy

But they make it look so confusing

[viscid thistle]

So we don't want 0's and negative numbers on the denominator, do you agree?
Remember this?

[grim sand]

U just threw them away?

[viscid thistle]

What are you saying lol

[grim sand]

It has -3 and a square root

But u just gave me 2x-1>0

[viscid thistle]

-3 doesn't affect the domain

[grim sand]

Urs look so simple

OH

[viscid thistle]

Okay listen to me

[grim sand]

So the top doesn’t have anything to do with the domain

If we’re looking for domain only focus on the bottom

[viscid thistle]

In this case, no

[grim sand]

Can u give me another random one

Like question 7

To see if I can do it

[viscid thistle]

Sure

[grim sand]

What’s a discontinuities

[viscid thistle]

Nvm

Domain of $y=\frac{4727}{x+3}$

[obsidian monolith]

Al𝟛dium:

[grim sand]

That’s a huge number

[viscid thistle]

What would you look at now

[grim sand]

Only x+3?

[viscid thistle]

I wanna test you on "does it matter if it's million on the denominator"

Only x+3?
Yes

So what we said earlier

[grim sand]

How’d u put the > in there

[viscid thistle]

What a denominator cannot have

[grim sand]

0

Or negative numbers

[viscid thistle]

Great

No

[grim sand]

Huh

[viscid thistle]

A denominator can perfectly have negative numbers

An sqrt not

[grim sand]

Do

[viscid thistle]

Look $\frac{1}{-3}$ does this have a solution

[grim sand]

So*

[obsidian monolith]

Al𝟛dium:

[grim sand]

Yes

[viscid thistle]

Well

Okay yeah

[grim sand]

But if it’s a square root

It can’t use negative

Yes?

[viscid thistle]

Yes

It does not have a real solution over the negative numbers, that's why

[grim sand]

What is a real solution

[viscid thistle]

But $\frac10$ does not exist

[obsidian monolith]

Al𝟛dium:

[grim sand]

Cuz u can’t simplify that

Right

[viscid thistle]

What is a real solution
Uh don't worry about it

[grim sand]

It can’t divide

[viscid thistle]

Yeah you can't divide by 0

[grim sand]

Yes

[viscid thistle]

So what we are gonna do with your problem is to ask the function: for which values of x, does the denominator equal 0?

Therefore, solving x+3=0 see?

[grim sand]

Umm

[viscid thistle]

Because as you said a denominator can't be 0

Domain of $y=\frac{4727}{x+3}$

[obsidian monolith]

Al𝟛dium:

[grim sand]

Yes so we use 0?

[viscid thistle]

We use to solve for the values of x that make the denominator 0

Therefore, solving for x+3=0

[grim sand]

Can it also be >or = to 0

[viscid thistle]

You can see yourself that x=0 is on the domain perfectly, $\frac{4727}{0+3}=\frac{4727}{3}$ see?

[obsidian monolith]

Al𝟛dium:

[viscid thistle]

Can it also be >or = to 0
The < or > are for square roots, we'll move there after

[grim sand]

My teacher always told me that X always = 1

[viscid thistle]

What?

[uncut mulch]

lol

[grim sand]

Like

X+X= 2x?

Back in algebra X by itself Is always 1

[uncut mulch]

you mean: $x = 1x$?

[obsidian monolith]

ramonov:

[grim sand]

Yes

[viscid thistle]

x is not always equal to 1 at all Jupiter

Oh okay

[uncut mulch]

x is 1x

if you insist

[grim sand]

So X=0 confuse me

[viscid thistle]

Please remember to read all my messages, i will repeat myself