precalculus

[hollow bluff]

I do not know how to start

[blissful wadi]

@hollow bluff study the limits in the domain bounds to find asymptotes

f(0) = interception with the OY axe

f(x) = 0

[hollow bluff]

OX axe?

[blissful wadi]

interception with OX axe

[hollow bluff]

so if f(0)= y?

[blissful wadi]

then the function intercept (oy) axe ( the vertical one ) at point y

[hollow bluff]

what is OX and OY

is that just locations on the graph?

[blissful wadi]

dont mind the question

[hollow bluff]

I havent heard or used that terminology before

[blissful wadi]

(ox) axe is the horiozntal

(oy) is the vertical line

[hollow bluff]

ok

[green zenith]

i want to find the domain of sqrt((x+2)/(x-3))

so it should be (x+2)/(x-3)>0 and x-3=0, right?

[blissful wadi]

x-3 =/ 0 yes

[green zenith]

yes. i wasnt sure how to type it.

so as for (x+2)/(x-3)>0, is it the same as equating?

[blissful wadi]

the intersection of the two intervals where x+2 and x-3 are positive

or the intersection where x+2 is positive and x-3 is positive and not equal to zero

intersection of the two intervals*

[green zenith]

hmm

i dont quite understant

understand

[blissful wadi]

[2- ; +oo [ (intersect ) ]3 , +oo [

and also the intersection where both are negative ( and x-3 is not equal ot 0 )

which is ]3 , +oo [ U ]-00 , -2 ]

[willow bear]

please don't write ∞ as "oo"

[green zenith]

its quite difficult to understand what youre typing, im not familiar with that kind of format.

but i did understand it

so do i just check it?

[blissful wadi]

@willow bear not used to writing on computers xD

[green zenith]

i can't equate it like (x+2)/(x-3)>0?

[blissful wadi]

u can also use ( x>3 and x<=-2 )

@green zenith yes u can

but its basically just the intersection where both are positive and both negative

at the end end its (where both negative ) U (union) ( where both are positive )

that way u'll save time and its more easy

[green zenith]

so that means that i check some numbers?

like x=-3,-2,-1,4, for example

[blissful wadi]

yes u can plugin a number from the domaine to check if its correct or no

[green zenith]

ah ok i got it now

thanks

[blissful wadi]

awesome

[tidal quest]

guys 😦 How can I draw a graph of y=(x-[x])^2

I tried using desmos 😦

but fail

[viscid thistle]

@serene heath I tried dividing them using long division and making their remainder equal 0

[stuck lark]

@tidal quest try y = (x - round(x))^2

[serene heath]

@viscid thistle plug in the root into both equation and equate to 0

[tidal quest]

@stuck lark it works thank you!

[stuck lark]

no prob

[tidal quest]

Should I use floor or round?

[x] is denotes the greatest integer less than or equal to x

[stuck lark]

@tidal quest nearest integer function (nint or round) is not the same as greatest integer function (floor)

[formal iris]

Can someone tell me why A is a horizontal shrink of 2

[charred hull]

on y = e^x, for x = 4, y = e^4; however, for y = e^(2x), y = e^4 when x = 2. the function kinda. advances faster/condenses so it's called a shrink @formal iris

[foggy nymph]

Not really sure how I can approach this 😅

[charred hull]

it's a combinations question

do you know how to do permutations and combinations etc?

[formal iris]

Does this apply only to expo functions? @charred hull

[charred hull]

no, it does not

think of y = x and y = 2x

[formal iris]

also is your name based on the AP sample question

[charred hull]

no it's not

[formal iris]

right 2x advances faster then x tru

so isnt that a vertical strech?

[charred hull]

nope

think of uhh

sine functions

with sin(x)

sin(2x) is a horizontal stretch

well

ok lemme add a qualifier

y = 2x is both a horizontal and vertical stretch of y = x

however, y = e^(2x) would be a horizontal and not a vertical stretch of y = e^x

[formal iris]

what do u mean isnt that a horizontal compression?

[charred hull]

yeah sorry *compression

got the words "shrink" and "stretch" mixed up

[formal iris]

Same with e^x vs e^2x it seems like horizontal compression

[charred hull]

yep

it's a horizontal shrink, sorry bout that

[formal iris]

oh yea that happens with me also

its fine. So is a shrink equal to compression?

[charred hull]

yeah

[formal iris]

No second question: when you describe horizontal transformation dont you use the inverse for the factor

E.g y=2x is a horizonal compression of 1/2 compared to y=x

[foggy nymph]

@charred hull sorry yes I do

[charred hull]

@formal iris yes

well

yeah sorta like that parth

ok so

for your question shadow

if you think about winning 3 out of 6 matches

do you think you can write those matches that are won as a combination?

[formal iris]

wait what do u mean sorta

😦

[foggy nymph]

Ok sorry before we get into that

I’m confused about the problems values

If 5/16 is the chance of a tie

Wouldn’t it be 5.5/16 for a win

[charred hull]

no

well

lemme check actually

[foggy nymph]

Cuz 11/16 is the chance that they don’t draw right...

[charred hull]

yep

[foggy nymph]

Oh is it right

[charred hull]

11/32 is the chance of winning for both sides

anyways back to the original question

how many possible outcomes are there for the match?

with equal odds at each round

(aka 1/2 for either side)

[foggy nymph]

64?

2^6?

I’m getting 15/64 + 6/64 + 1/64

So it’s 11/32

.....

I’m lost again

[charred hull]

okay sorry bout that

was busy for a sec

yes, it's 64

now you're selecting 3 of those wins out of 6, right?

[foggy nymph]

Yeah

[charred hull]

so select 3 wins out of 6 matches with either a permutation or combination then

[viscid thistle]

how do you write a sine function with amplitude 3 period 4 pie phase shit pie/4

nvm

F(0)=320 is the last part

I don't understand why I was wrong

[trim fable]

I have a question

how are the functions f(x)=x+n and g(x)=1/x+n related?

[limber bone]

they are not ig?

[viscid thistle]

in what context

[limber bone]

wdym related

[trim fable]

like this was

an investigatiion for linear functions and their

reciprocals

[viscid thistle]

i suppose they are both equal at x=1

[trim fable]

thats all?

coz theres like 6 similarities I have to find

i think

coz theres 6 points

lol

[viscid thistle]

yikes

ok

[trim fable]

lol

[viscid thistle]

is it 1/(x+n) or 1/x +n

[trim fable]

uh

no brackets

does that make a difference?

[viscid thistle]

yes

[trim fable]

oh ok

[viscid thistle]

you could mention their symmetries

[trim fable]

ok

[viscid thistle]

they are both symmetrical across the line x+n

and symmetrical across the line -x+n

[trim fable]

ok

[viscid thistle]

they are both are odd functions when n = 0

which is a cop out but idk

[harsh stag]

Hey, guys. I have a quiz for Pre-Calculus tomorrow and I wanted to know if any of you have any good videos to review the following concepts??

[viscid thistle]

@serene heath sorry wdym by "plug in the root"?

[static kettle]

Yo, I'm 29 but something tells me my math brain is at a level of 5... so bare with me... I'm trying to write equation from math to python... but I got stuck on one symbol.. its bezier...

((1-t)pointA.x+tpointB.x,(1-t)pointA.y+tpointB.y
translates to
((1-value)pointA.x+valuepointB.x , (1-value)pointB.y +tpointB.y)

what I'm lost with is the "," in between the 2 equations... what does it symbol in math?

wait, thats vec2 item, so left and right number... ehhhhhhhhhhh

[willow bear]

nothing in particular. here it just separates the x and y coordinates of your point

or 2D vector

whatever

[static kettle]

yeh I just realized it, sigh. thanks!

Hmmm does this:
(1-t)pointA.x translates to (1-t)*pointA.x ?

or is that pow ?

[hoary valley]

If the original function became like the one at the bottom. Do we say It Reflected About The X-Axis ? or what ?

[static kettle]

reflect Y

[serene heath]

@viscid thistle plug in -2, it's a root cuz x+2 is a factor

[willow bear]

@hoary valley no, this is a reflection about the y-axis

[static kettle]

And I'm lost...

The dotted lines should not go straight, but up, yet they go straight... what did I mess up o.O ?

wait

I'm a nub.

it works.

nvm

sigh

[hoary valley]

How To know whether this function Even , odd or neither

[stuck lark]

https://lmgtfy.com/?q=definition+of+odd+and+even+functions

[hoary valley]

I know but I mean if it's a Log function @stuck lark

[stuck lark]

what do you think, then?

[willow bear]

@hoary valley log is defined on (0, +infty)

that is not a symmetric domain

therefore it makes no sense to speak of whether or not it is even or odd

neither concept applies to it

[hoary valley]

@willow bear Oh really helpful information.. Thanks Ann.

[willow bear]

i did nothing worth thanking for but ok

[hoary valley]

Are these equal ?

[willow bear]

no

not even close

log_e(1) = 0 while e^1 = e

no these are not equal

[serene heath]

Hmm

Wonder what values of x make that true

Nvm just remembered shape of their graphs

[hoary valley]

The exponent (x) is positive... so why is it on that side ?

[serene heath]

Wdym

[hoary valley]

I know if the exponent (x) is positive it should be on the other side.

like that

[willow bear]

no

"you know" but you're wrong

the condition isn't positivity, it's being greater than 1

[hoary valley]

Right..

[willow bear]

if you try to graph y = c^x for c < 0 you'll just fail

[hoary valley]

I tried, and it reflected over the X axis

It went down

[willow bear]

if you tried -2^x then that's not what i meant

-2^x is not (-2)^x

[hoary valley]

Is there a quick way to find out if it's True or False?

Uh

[forest seal]

take log to both side

[royal shard]

@hoary valley are you not sure how to progress?

no don't do that, it's way simpler

simply recall that $\frac{1}{a^{-b}} = a^b$ and $64=4^3$

[obsidian monolith]

ukdl:

[hoary valley]

I solved it but it took me like 2minutes

[royal shard]

that should get you all the way there

ok

[hoary valley]

Thanks bud

[royal shard]

np

[sleek pawn]

hi

so I'm stuck on this problem bc I'm not sure what model to use

it's about a string of emails or something

[near ledge]

need some help with linear and quadratic inequalities

[sleek pawn]

r=4
a1=8
and they want me to get the "resent" at which every user on the network (7 323 557 942) will recieve it

oh

[near ledge]

am i looking for the y coordinate ?

like it wnats me to know a set of values for say x^2 -1 > 0

i'm so lost

[sleek pawn]

well I think you should find x

there's no y in that inequality

[near ledge]

yeh i can find x easy that aint the problem

my problem is it's asking for a set of values

what damn set of values

[sleek pawn]

:/

the root doesn't give you a plus minus value or anything?

[viral imp]

,, \frac{1}{4}\log_8{(x^4+2x-6)}=\log_8{x}

[obsidian monolith]

Umma.Gumma:

[viral imp]

so, in order to solve this equation I should verify for which values x^4+2x-6 > 0

I'm not really sure how to proceed. If if were x^4+2x^2-6 it would be ok

this form looks nasty though

[serene heath]

What can u do with the lhs

[viral imp]

with what?

[vague zephyr]

would someone be able to tell me how to find the x-y coordinates for angles on a unit circle?

[serene heath]

@viral imp the left hand side

[vague zephyr]

what do you mean

[viral imp]

ok, you mean raising the log argument to the quartic root I guess (1/4)

[serene heath]

Yea

Then u have log_8(stuff)=log_8(x)

Can u see where to go now

[viral imp]

yeah sure, what I tried to do was getting rid of the fraction multiplying by 4 both sides

but couldn't verify the log argument

[serene heath]

Yea that gives the same.thing

Wdym by log argument

[viral imp]

I mean, once I get rid of the fraction, I am left with the infamous x^4+2-6 > 0

without chance to take the path you suggested

[vague zephyr]

nvm my friend helped me

[sleek pawn]

hey can I get some help with exponential functions?

[viscid thistle]

yeah sure

[sleek pawn]

so I have an initial condition of 8 people, each one of them will send an email to 4 people and there's a total of 7,323,557,942 people on the network. Supposing that they have 1 hour max to send the email and everyone follows the instructions, how long would it for everyone on the network to receive it?

[obsidian monolith]

A regular kugelblitz:

[sleek pawn]

but there's no time variable involved...

[viscid thistle]

ok lets see here

how much time per email?

[sleek pawn]

1 hour

[viscid thistle]

oh so they take 1 hour to send the email?

ok i guess

why did you use geometric series formula?

[sleek pawn]

oh should it be n?

[viscid thistle]

oh i see

[sleek pawn]

because that's the one they told me to use

[viscid thistle]

ok so solve for n

that would be time

[sleek pawn]

oh that's simple then, bc they had asked me the number of times the email had to be sent to be received by everyone just in the last question

and it was n as well

ngl, I don't fully understand the formula

[obsidian monolith]

A regular kugelblitz:

[viscid thistle]

yr

yes

[sleek pawn]

ok, thank you

[viscid thistle]

wait no

no no

divide by 8

[sleek pawn]

?

[viscid thistle]

then add 1

not add 1

then divide by 8

[sleek pawn]

ohhh

see, that's what made sense to me, but my teacher showed a similar example with different values and she put the addition before the division

smh what a weird teacher

hmmm

how come I get the same result?

well the approximation might've been off in the decimals

anyway

thank you!

oh wait

so in another question they ask me to get the geometric progression of a term

is this alright?

[obsidian monolith]

A regular kugelblitz:

[sleek pawn]

because it should give me the number of users that are receiving the email at reply number 9.3632, which is the last reply, but the result is < 0, which doesn't convince me

[harsh cipher]

Hi

Why is d not a polynomial?

d)

sorry I meant e)

[sleek pawn]

I asked a question <@&286206848099549185>

[serene heath]

@harsh cipher u need to have integer powers

[sleek pawn]

can someone please help me?

[harsh cipher]

@sleek pawn I know. He explained there's power of 1/2 which I didn't understand.

[clear glade]

what's this formula called

oops P(t) was cut off

[hollow bluff]

So with using the odd root property can someone explain how they went from this step to the next

[stuck lark]

$3^4=81$

[obsidian monolith]

RokettoJanpu:

$3^4=81$

[hollow bluff]

ok

I think i understand

[slow roost]

I dont get why its set up like that lol...

[trim fable]

hiii

can someone help me

[viscid thistle]

tan theta = -8/9 find cos theta

[viscid thistle]

same

I cant find anything online

that helps

[grave gate]

Well you can square the tan theta to get 64/81

[viscid thistle]

see ik

[trim fable]

question guys

[viscid thistle]

what is it

something + x^2 = 1

maybe in inverse

i sqaured it now what

@grave gate

[grave gate]

Use the identity tan^2 theta+1=sec^2 theta

[hoary valley]

What's the difference between " an increasing on (0,+infty)" and " an increasing on R" ?

[limber bone]

increasing on (0 , infinity) well

means its increasing on this interval

all positive real numbers i g

R is (-inf , inf)

[hoary valley]

@limber bone F(x) log_3 X is increasing on what?

[limber bone]

what?

well

you see

find F'(x)

and you tell me

but

i know that

the domain of this function

is not R

[hoary valley]

Right

domain is (0, + infty)

@limber bone In my opinion it's increasing on R , but apparently that's wrong.

[limber bone]

it cant be increasing on R

cuz its not even defined on R

all of it

[hoary valley]

Because it's coming from -infty and going to +infty.

[limber bone]

you cant plug in negative numbers

in this

this is outside of your domain

[hoary valley]

@limber bone But look man, it's coming from down there and going all the way up..

[limber bone]

yes

but the interval of x

that makes this true

is not (-inf , inf )

[hoary valley]

@limber bone Wait so when we say a function is increasing on (5, +infty) this means it's only increasing when we insert the x values from (5 to +infty) ?

[limber bone]

yea

pick x_1 and x_2 from (5 to infinity)

we know that

[hoary valley]

Interesting.. so we talk about X values that makes it increase or decrease

[limber bone]

if x_1 <x_2 ---> f(x_1) < f(x_2)

yea

thats WHERE your increasing

on your domain

[hoary valley]

Thank you @limber bone

❤

[limber bone]

np

[hoary valley]

The domain of any similar function that has a positive sign will always be R .. Right?

[flint river]

indeed

no restrictions here

[hoary valley]

@flint river even if the exponent was negative 5?

[flint river]

right because in that case a very big number "will turn that" into a value very close to zero

if the second term was negative the story is different

*were (I guess)

[hoary valley]

Yeah I know @flint river thank you.

[rigid sun]

no problem

[hoary valley]

I know if it's a line function like the one in the numerator then sure it is a one to one function, but the X in the denominator confuses me. help

[rigid sun]

what does the graph look like?

think about it

[viscid thistle]

I have to simplify this so far the only step I get to is -cot^2(x) at the bottom

on denominator

[rigid sun]

check your work

you got it

[viscid thistle]

I've been stuck trying to wrap my head around next step from there

am I suppose to convert the cot ?

cos(x)(1-csc(x))/-cot^2(x)

[rigid sun]

divide it out

put things in terms of sin and cos

[viscid thistle]

wait is 1-csc^2(x) cot^2(x) or -cot^2(x)?

[rigid sun]

-cot

[trim fable]

hey guys

can someone help me in probability and statistics

[viscid thistle]

I would have to distribute the cos(x) to (1-csc(x)) at the top?

[hoary valley]

I plugged the 4 into the G function and got 5... but then I can't plug it into f , since f(x)= is just 7 it doesn't have a variable x

Help

[willow bear]

what do you mean you can't plug that into f

sure you can

you'll get 7

f is a constant function

[hoary valley]

yeah it's a line at 7

[willow bear]

f(x) = 7 means that no matter what value of x you plug in

you get 7

f(1) = 7

f(56234) = 7

f(72368923457329846732896.45734673862349867293485623+π) = 7

[hoary valley]

Uh Thanks

[willow bear]

i mean

if you're so eager for an x to plug your thing into

$f(x) = 7 + 0x$

[obsidian monolith]

Ann:

[hoary valley]

Amazing!

[hoary valley]

Is this true ?

When I graph it , it looks like it has a vertical asymptote at 0

[willow bear]

it does indeed have a vertical asymptote at x=0

[hoary valley]

This should equal 8 ,right?

[willow bear]

idk, should it?

[hoary valley]

I think so, but I'm not confident in my answer.

[glacial island]

yea

[willow bear]

@hoary valley what makes you not confident in your answer?

[hoary valley]

Idk I've never answered a similar question, I guess.

All 4 answers are rational functions...

[willow bear]

no

only one is

"rational function" does not mean "has a fraction"

[hoary valley]

...

[willow bear]

what do you think a rational function is

[hoary valley]

I know it looks like this.

[willow bear]

no

not all rational functions' graphs resemble that of 1/x

and that isn't what i asked you for

what is the definition of a rational function?

[hoary valley]

1/x^2 is rational as well?

[willow bear]

yes 1/x^2 is also a rational function but that isn't what i asked for

[hoary valley]

Do functions have definitions ?

[willow bear]

EVERYTHING in math has a definition

[hoary valley]

I know how they look and what their equations are..

[willow bear]

i'm asking you to give me the definition of the word "rational function"

[hoary valley]

I don't know..

[willow bear]

then you don't know what a rational function is

look it up

[hoary valley]

In mathematics, a rational function is any function which can be defined by a rational fraction..

[willow bear]

...where tf did you get THAT from

[hoary valley]

https://en.wikipedia.org/wiki/Rational_function

[willow bear]

how nice of you to omit the key part of that sentence!

[hoary valley]

😂

[willow bear]

...a rational fraction, i.e. an algebraic fraction such that both the numerator and denominator are polynomials.

[hoary valley]

But 1/x doesn't have a polynomial on the numerator

[stuck lark]

constants count as polynoms too

[uncut mulch]

c = c*x^0

[hoary valley]

Oh man, This is interesting stuff.

Ok let's start with the 1st one, in my opinion it is a rational function..
Because both the numerator and the denominator are polynomials. 1x^0 - sec(x) / 3x^0 + sin(x)

[uncut mulch]

what's your definition of a polynomial?

[hoary valley]

A variable and you just told me it can be a constant number

[willow bear]

no

you don't know what a polynomial is either

[hoary valley]

That function fulfills every written condition here..

[uncut mulch]

even that last part?

[hoary valley]

It doesn't have any exponents

[uncut mulch]

is sec(x) a non-negative exponent of the variable x?

[hoary valley]

There are no exponents .

beside 0

[uncut mulch]

that isn't really answering the question
can sec(x) be expressed as x^a where a is a non-negative integer?

[hoary valley]

Yes, we can use 0 and then It will become 1

[uncut mulch]

sec(x) isn't 1

[hoary valley]

It's not but It can be

[willow bear]

no

[hoary valley]

Ok I have a question is " 1 " a variable ?

[wraith idol]

um can it "vary"?

[hoary valley]

in a way yes

[stuck lark]

1 is a constant but can be thought of as the coefficient of a 0 degree term. quoting ramonov from earlier:

c = c*x^0

[uncut mulch]

but you can't write sec(x) as a non-negative integer power of x

[hoary valley]

0 is considered a positive number

[uncut mulch]

no

its neither negative nor positive

[hoary valley]

Ok I think this one is also a rational function.
The reason for that is. It has polynomial on the numerator and on the denominator.
The 3 is a poly.
X-1 is a poly.

[wraith idol]

no

[uncut mulch]

x-1 is a poly
but sqrt(x-1) is not

[wraith idol]

is x-1 the denominator tho

[uncut mulch]

can sqrt(x-1) be expressed as x^a where a is a non-negative integer?
if you think it can, tell me the value of a.

[willow bear]

you can't just ignore the square root...

[hoary valley]

Well, Is this a rational function?

[uncut mulch]

using those rules, what do you think?

[hoary valley]

Well yes it's rational.

[uncut mulch]

yes, it is.

[hoary valley]

What we call this function?

[willow bear]

what do you mean

i guess you could call it a power function

[hoary valley]

I know e^x is called the natural exponential function.

[willow bear]

where the power just happens to be e

[hoary valley]

Ok

What we classify this function as ?

In my opinion it's an exponential function or natural exponential function

[willow bear]

no

it's not

it's a constant

[hoary valley]

Oh, cuz it doesn't have a variable..

So it's just a line

What we classify these two functions as ?

I can't graph them

I don't see X

Constant like e^2

Thanks Jy1852

@blazing monolith If it's ln x < natural logarithmic function, right?

[regal spade]

would equations be considered precalculus?

cuz I'm very confused with something that probably has a stupidly simple answer

0*x = 0
can be:
x = 0/0
or:
0 = 0

and I don't understand what this means mathematically for any X

or how that function works

[serene heath]

Erm what

Can u rephrase

[regal spade]

0 = 0 makes sense to me

[serene heath]

Ofc

[regal spade]

I still don't understand where x comes in though

because I got 0 = 0 from solving(?) an equation
which has an x

[serene heath]

0 *x = 0 is true for any x

So u cant really solve for x

Which makes sense cuz u csnt divide by 0

[regal spade]

so it's an equation that

is impossible?

like whatever/0 makes sense to me

I watched a video on it

in that it can't really be defined as anything

because there's a lot of things it could be

whatever/whatever is 1, so it could be 1

if you divide a positive number by smaller and smaller numbers it's infinity

negative is negative infinity

so I understand why whatever/0 can't work

but now it doesn't make sense in my head that "x" in a function can't work

like if I try to give x a number in the original equation

what does that give me?

a statement saying 0 = 0?

[serene heath]

Where are functions coming from

Theres no function here

[regal spade]

no sorry

equation

[serene heath]

Yea

Plug in any x whatsoever

Ur equation still holds

[uncut mulch]

whoops misread that as ^

[serene heath]

All good

[regal spade]

123 = 0/0

[serene heath]

No

Where did u get that from

[regal spade]

0*x = 0 (=) x = 0/0

it's multiplying on one side so I can just divide it on both

[serene heath]

0/0 is undefined u cant just set a random value to it

[regal spade]

precisely my point

0*x = 0 (=) x = 0/0

so is this ^

impossible

or wrong

ooooh

it is

because 0/0 isn't 1

so it wouldn't be x = whatever

(0*x)/0 = (0)/0

doesn't equal

x = 0/0

because you can't cut the zeros on the left

since 0/0 isn't 1

so it's impossible to get just the x on that side

aight fun stuff

thanks

[serene heath]

Not sure what I did but np

[viscid thistle]

How do we get from the first step to the second step, I'm trying to simplify but not sure how this example reached this conclusion

[serene heath]

They multiplied top n bottom by cotv

[viscid thistle]

to cancel out the fraction?

[serene heath]

Yea

[viscid thistle]

What would I do with the denominators to be able to add them? I'm stuck in this step

sin(x)+cos(x) we can't add yet because of -sin(x)-cos(x)

[ruby frigate]

you can take out a -1 from the denominator and move it out front

[viscid thistle]

so it would be -1(sin(x)+cos(x)) after?

[ruby frigate]

yes but you can also move it to repalce the + with -

[viral imp]

Is this correct so far? not sure how to proceed

please consider the page lower half only

[ruby frigate]

go back to the middle line where you got 2-3^x=3^-x

see if it makes it easier if you replace 3^x with a random variable

people generally use u

[viral imp]

nice, therefore 3^-x would be 1/u right?

[ruby frigate]

yes

[viral imp]

thanks will try right now

great it was easy after that step

thanks a lot

[ruby frigate]

np

[viscid thistle]

so I got the first part and after we find the common denominator we have to cross multiply right?

I would distribute the cos(t) to the (1+cos(t))?

[gentle vigil]

Yes

[formal iris]

Can someone help me with 73 I have never proved anything every

ever**

[rigid sun]

Lol who wrote your book

Cus they’re sped

[formal iris]

Idk what a sped is

is that bad?

[rigid sun]

Yes

[formal iris]

why is the book bad

[rigid sun]

73 is not possible

[formal iris]

why is that

[ruby frigate]

they usually have solutions for odd questions in the back

what did they put?

[formal iris]

let me check

[rigid sun]

Lol that literally makes no sense

[formal iris]

goes to only 65

[gentle vigil]

Why is it not possible? @rigid sun

[rigid sun]

Lol pranked

[formal iris]

Yes im pranked

#epic

[serene heath]

What's the fraction? Cant zoom on mobile

[rigid sun]

lim x—> -inf of b^x is 0

[formal iris]

I can show u

[rigid sun]

how is c/1=0

boi

[formal iris]

C/(1+a*b^x)

lim x goes to - inf (C/(1+a*b^x))

[serene heath]

Ok yea

U wanna prove that?

[rigid sun]

Oh wait I’m sped

[formal iris]

Yes !

[rigid sun]

Nvm

[serene heath]

Oh yikes

[formal iris]

is that hard?

[rigid sun]

I couldn’t read the last part

It was blurry

[formal iris]

Maybe you have learned to not call people autistic now

[serene heath]

Do they want limit def?

[formal iris]

limit def? Is that a defined limit?

[serene heath]

The epsilon delta stuff

[formal iris]

Im in precalc

👀

[rigid sun]

[serene heath]

Then what does it mean by prove

[formal iris]

i think it means like show

now my issue is b^-inf is just 1/inf

[serene heath]

Are u sure

B<1

[formal iris]

yes oh shoot

that makes b really small !

[serene heath]

@spring thunder what do u think of my name

[spring thunder]

[serene heath]

Wait did I spell it right

Ok I did

Epix

[spring thunder]

but Ann changed her name back to normal

so the chain is fooked

[serene heath]

Wow

Betrayal

[spring thunder]

and tuong also lel

[serene heath]

[spring thunder]

we're the only two here now

[serene heath]

It's ok we can carry on the legacy

[frozen needle]

[serene heath]

[formal iris]

i got the thing guys its ok now thanks thp

[green zenith]

i need some help understanding absolute values

[ruby frigate]

by definition its the distance from 0 on the number line

[green zenith]

what do you mean

oh the distance. i get it.

but i have some equation that is confusing me

[ruby frigate]

show it

[green zenith]

how come the inverse of f(x)=|x|,x>/=0 is f^-1(x)=x,x>/=0

[gentle vigil]

Because |x|=x for x>=0

[green zenith]

i think what confuses me also is how i get the inverse. how do i solve |y|=x?

[gentle vigil]

Yes, in principle you have to solve it

[green zenith]

yes, i want to understand it so i dont get confused everytime i see it.

[gentle vigil]

But it makes no sense to find inverse of a many-one function

Though in your domain (x>=0), absolute (x) is one-one

And absolute(x) =x itself

Do you understand that?

Absolute of any positive number is that number itself

And absolute of any negative number is negative of that number

[green zenith]

so |y|=x isnt a function?

i didnt even understand how i get the domain of the inverse function.

[gentle vigil]

It is a function

Domain of an inverse function is range of original function

But that's not what I used here

[green zenith]

oh yeah thats what it was

and i do understand what you meant earlier

and i see the function geometrically

[gentle vigil]

Yes that's helpful

[green zenith]

cos the f(x)=|x|,>=0 is the line y=x from 0 to infinity

so inversing it, it's |y|=x, y>=0.

so is it because y>=0 that it is only equal y=x?

[gentle vigil]

Yup

[green zenith]

ahhh

but what about without the conditions?

is that still a function and an inverse function?

[gentle vigil]

You can't find it's inverse without this condition

Because that function is not invertible (one-one and onto)

[green zenith]

oh yeah thats right

and its also not a function, right?

okay

thanks for helping

[gentle vigil]

It is a function

@green zenith

But not all functions are invertible

[green zenith]

wait, |y|=x is a function?

[gentle vigil]

x is a function of y there

But yes, y is not function of x

[green zenith]

so this is f(y)=y?

could it be solved that |y|=x is a function of y?

[gentle vigil]

For y>=0

[green zenith]

ahhh. that is the condition so that that could be a function.

okay

[gentle vigil]

Yup

[green zenith]

i have another different question

[gentle vigil]

Sure

[green zenith]

is the inverse function of f(x)=x^2+1,x<=0 is f^-1(x)=sqrt(x-1), x>=0?

is this correct?

[gentle vigil]

No

$-\sqrt{x-1},,x\geq1$

[obsidian monolith]

oscillatingEquilibrium:

[green zenith]

wtf

[gentle vigil]

Why would there be a negative sign? Do you see that?

[green zenith]

yeah i see the negative sign. is it because its x<=0?

[gentle vigil]

Yes

And what is range of f?

[green zenith]

[1,infinity)?

[gentle vigil]

Yeah

So there you go

[green zenith]

ah

so x>=0 is sort of the domain

[gentle vigil]

Of?

[green zenith]

of f(x)

[gentle vigil]

x<=0 is domain of f

[green zenith]

oh yeah mb

so that is the domain, and range is y>=1

[gentle vigil]

Yes

[green zenith]

and range is the domain of f^-1(x)

[gentle vigil]

So range of function is domain of inverse and vice versa

Yup

[green zenith]

but how did you get the inverse function?

why is there a minus sign?

[gentle vigil]

$ f(x)=x²+1=y\
x² =y-1\
x=\pm\sqrt{y-1}\
$
But, domain of x is $x\leq 0$, so + sign is disregarded

[obsidian monolith]

oscillatingEquilibrium:

[gentle vigil]

Hence, $f^{-1}(y)=-\sqrt{y-1}$

[obsidian monolith]

oscillatingEquilibrium:

[green zenith]

ahhhh

so it is because the range of f^-1(x) or the domain of f(x) is >=0 and x = +/-sqrt(x-1).

ayayay

so if there wasnt any square root, my sign would stay the same regardless of < or > signs?

[gentle vigil]

Yes

[green zenith]

ahhhh okay

thank you

its still hard to integrate in my brain. xD. i need more practice.

[gentle vigil]

Good luck!

[viscid thistle]

I'm trying to simplify this problem, so I know the denominators cancels out when dividing, but what would be the next step after this?

[gentle vigil]

There can be many answers to this

[patent beacon]

You're done with canceling that, I assume

[gentle vigil]

You can just write whatever is left after cancelling

Or you can substitute trigonometric identity too

[patent beacon]

Oh wait, there is sin²(u) + cos²(u) = 1

Do they want that too?

[gentle vigil]

I don't know

And it's also possible to factorise numerator (only to find out it doesn't cancel anything)

@viscid thistle try those options out

[viscid thistle]

yea

[gentle vigil]

How will you go about solving it?

[viscid thistle]

I worked my way down to that part

where I cancelled denominators

[gentle vigil]

Oh okay

You can use trigonometric identity now

sin²(u) + cos²(u) = 1

[viscid thistle]

wait with the one I still have to find lcd

right?

[gentle vigil]

Lcd?

[viscid thistle]

least common denominator because after cancelling its

[gentle vigil]

x/1 is just x

[viscid thistle]

sin²(u)-cos²(u)/sin²(u)+cos²(u) +1

[gentle vigil]

Yes

But sin²u+cos²u=1

[viscid thistle]

so bottom turns to 1

[gentle vigil]

Yes

[viscid thistle]

sin²(u)-cos²(u) + 1?

[gentle vigil]

Yup!

So now what's next?

Can you do something about last 2 terms?

[viscid thistle]

split them up right?

A^2-B^2?

[gentle vigil]

No

What is 1-cos²u?

[viscid thistle]

sin^2u?

[gentle vigil]

Yes

[viscid thistle]

so its sin^2u+sin^2u add like terms then we get our answer nice

[gentle vigil]

Yeah!

[viscid thistle]

I can do that even if they where grouped together?

the sin and cos

before adding the 1?

like we cancelled the fraction but why can we add the 1 if it wasn't part of it to begin with you know? still confused on that haha

[gentle vigil]

Yes you can do that.

(a+b)+c =a+(b+c)

Right!

[viscid thistle]

ah okay noted thank you for the explanation it was wonderful writing it to my notes

[gentle vigil]

I'm glad!

[viral imp]

,, \log(4^{1-x}+2)-\log(2)=\log(2^{2x+1}-3)

[obsidian monolith]

Umma.Gumma:

[viral imp]

I'm going through this equation. As far as I understood, before proceeding with calculations it would be appropriate to check that all log arguments are > 0

the point is, 4^{1-x}+2 seems to fail this check

the main equation has a solution though

[last violet]

It's not particularly important to check that the arguments are greater than zero

Imaginary numbers aren't bad

[viral imp]

yes, but I'm not supposed to work with C at the moment

[last violet]

What's the objective, just to find x?

[viral imp]

yes

[last violet]

Is log the natural log?

[viral imp]

no, it's base 10

[viral imp]

Is this correct? I get to a point where it's not clear what should be done

[proud sparrow]

if it is correct, x would be noninteger

[viral imp]

sorry what

[proud sparrow]

line 6

3*2^x*2*3

[viral imp]

what is the issue here

[proud sparrow]

suddenly a second factor of 3 appeared

[viral imp]

you're right

there should be only one

[proud sparrow]

but x still seems noninteger

[viral imp]

I mean, even correcting that I assume I would get stuck in something similar to the last line

[proud sparrow]

did you copy the question correctly?

[viral imp]

yes

and, checking on wolfram, the correction you suggested leads exactly to the expected solution

[proud sparrow]

I'm really lost where the issue is

looks like x is really noninteger

[viral imp]

the last line is

,, 2^{x}(-\frac{11}{2})=3^{x}(-\frac{26}{3})

[obsidian monolith]

Umma.Gumma:

[proud sparrow]

well, we can move the constant factors together

[viral imp]

this, according to wolfram, gets to the solution

how to isolate x here is quite a puzzle for me

[proud sparrow]

well you can move the 2^x and 3^x to one side

and move the rest to the other side

[viral imp]

how? they're factors

[proud sparrow]

divide by 3^x

[viral imp]

nailed it

thanks a lot

[green zenith]

Are graphs that are symmetric about the x axis are functions? I thought when a vertical line passes through more than one point of the graph is not a function.

[blissful wadi]

wut ?

[green zenith]

Graphs that like that one in the middle

@blissful wadi

We use the vertical line test to test if a function or not geometrically, right?

[blissful wadi]

first one is symetric by the Y axis

the 2nd one by X axis

the 3rd by the center O

[green zenith]

Yes i know that. But is the second graph a function?

[blissful wadi]

yes

[uncut mulch]

2nd graph fails the vertical line test

[green zenith]

Yes it does

And im confused what does it mean

[uncut mulch]

I thought when a vertical line passes through more than one point of the graph is not a function.

well more specifically
y is not a function of x

however it does pass the horizontal line test so
x is a function of y

[green zenith]

So te inverse function is a function but the other isnt?

Y is not a function of x means that therr isnt any function, right?

[uncut mulch]

can't have an inverse function if the original equation isn't a function

[green zenith]

Ayayay

So just the function then of f(y)=y is a function?

[rigid sun]

yes

Bot it’s the same thing as f(x)=x

math sorcery

[hybrid charm]

(y)=y/f

[patent beacon]

(y)f = y

[rigid sun]

(=)y f y

[green zenith]

Now im more confused

My lvl1 brain cant process complicated maffs

[viral imp]

,, \sqrt{log_{\frac{1}{3}}|25-x^2|+2}

[obsidian monolith]

Umma.Gumma:

[viral imp]

should I consider +2 as part of the log's argument?

[patent beacon]

No

[viral imp]

is there a specific rule for this?

other than expecting all args to be included in parentheses

[thin heath]

Can someone help me factor this degree 3 polynomial by using an area model

I'm not sure how to do the other boxes

[willow bear]

x * ? = 10x^3

the answer to that goes on top of the first column

[thin heath]

Ok I wrote 10x^2 there

[willow bear]

likewise you can fill out the spot on top of the first column

[clear glade]

$100=(730)/(10(e^(-0.02t)))$

[obsidian monolith]

Waterblade:

[clear glade]

How can I start solving this

[willow bear]

uh

$100 = \frac{730}{10e^{-0.02t}}$

[obsidian monolith]

Ann:

[willow bear]

this?

[clear glade]

yes

[willow bear]

what have you tried

[clear glade]

multiplying each side by 10 then diving by 730 on each side

[willow bear]

and that gave you what

[trim fable]

hi is someone able to help 🙂

[willow bear]

move to another channel @trim fable

this is occupied

[trim fable]

umm what

[clear glade]

it gave me something along the lines of ln 100/73

[willow bear]

no like

no

[clear glade]

i forgot the exact answer, I erased it

[willow bear]

that is not what i asked you for

[clear glade]

oh

wat

[willow bear]

you said you multiplied by 10 then divided by 730 on both sides

what did you end up with after doing that

[clear glade]

oh

took natural log

[willow bear]

no

no that's not what i'm asking for

are my questions that hard to answer

[clear glade]

yea

[willow bear]

are they worded this confusingly

[clear glade]

yes

jk

[willow bear]

OH COME ON

WHAT THE FUCK NOW

[clear glade]

I erased my answer so i forgot what I did

[willow bear]

then redo the thing

[clear glade]

ok

ok

i got it

so

you want to know the steps I did everything in right?

[willow bear]

if you want me to check your work then you'll need to show me all of it yes

[clear glade]

ok

First I divided 730/10

on each side

[willow bear]

no

i said show

not tell

[clear glade]

no u

[willow bear]

don't "no u" me

are you not able to take a picture of your work

and send it here

how hard can that be

[clear glade]

ok

sorry wrong pic

[willow bear]

wow

fuck you

yeah no too late i screenshotted that

[clear glade]

wrong pic my bad

ok

thanks for helping me by swearing at me

[serene heath]

[willow bear]

you kinda drained my patience real fast with that question-dodging thing

[clear glade]

I just wanted help

ok Im sorry

[willow bear]

you kinda drained my patience real fast with that question-dodging thing

i am almost certain you aren't

[clear glade]

I really didn't understand u at first

why you kept telling me to stop I mean

I didn't question dodge intentionally

[trim fable]

hey Can someone help me

with 1a lol

so i can learn to do these

ill do the rest on my own i just dont get this

[patent beacon]

The y intercept happens when x = ...?

[trim fable]

0

i got that

and the domain is

[patent beacon]

Oh IC

[trim fable]

x|xcant equal 0

and y|0<y<=0.2

btw why does it say

[viscid thistle]

Why can't x=0?

[trim fable]

domain and range twice

coz it never touches x

right?

[torn oriole]

whomstve pung

[trim fable]

lol

[patent beacon]

The domain is the set of all x-values you can put into the equation

[trim fable]

hehe me

[torn oriole]

sorry i went afk

lol

[trim fable]

oh ok

[patent beacon]

There's some values that cause problems

[trim fable]

question