Domain, & Range of a Function

[spice ingot]

Won’t this domain be all real numbers, & the range: all real numbers, more than - 9.

[spice ingot]

• I meant more than -3

[shadow comet]

well

lets say x=4

what can y be?

assuming its all real numbers

[spice ingot]

OOOO

Dam yea

I guess it can be a negative

[shadow comet]

yes but to what extent

because remember

a square of a real number cant be negative

sooo

if x^2 or y^2 is greater than 9

then the equation wont be true

[spice ingot]

No but

Wdym

Won’t we have to

Re-arrange

[shadow comet]

wut

wdym rearange

[spice ingot]

Y = sqrt of( 9 -x^2)

[shadow comet]

yes

but

the thing in the square root

cant be negative

[spice ingot]

Ik

[shadow comet]

yea

so what if

x>3

[spice ingot]

But do we choose

[shadow comet]

or x<-3

[spice ingot]

I’m confused

[shadow comet]

and plus

this isnt a function

[spice ingot]

Whenever we sqr a number

[shadow comet]

this is an equation

so i dont get what ur trying to ask

[spice ingot]

Were allowed to assign a negative or a positive

[spice ingot]

Yeah, it’s not

I’m trying to find all the range values

And domains

[shadow comet]

bro what

range would always be 9 then

[spice ingot]

How?

[shadow comet]

bc the result is always 0

8

9

mb 9

[spice ingot]

BRO

I’m so confused

But whenever

[shadow comet]

YOU CANT FIND DOMAIN OR RANGE

[spice ingot]

U re-arrange

[shadow comet]

OF A FUNCTION

[spice ingot]

An equation

U CAN FIND

SUM DIFFERENT

ABOUT IT FROGG

[shadow comet]

wdym

bro

[spice ingot]

like

[shadow comet]

its an equation

the sum is always 9

[spice ingot]

Look

[shadow comet]

or do u want

x+y

[spice ingot]

This is what the textbook

Says

Range is -3 to 3

The same is for domain

Howww

Does that make sense

[shadow comet]

ohhh

bro...

[spice ingot]

Square root

[shadow comet]

i thought x and y were just variables

[spice ingot]

I think

[shadow comet]

💀

yea

[spice ingot]

Frog

I really don’t know too

[shadow comet]

if u make y = f(x)

[spice ingot]

Lol

[shadow comet]

it becomes

[spice ingot]

Okay

[shadow comet]

f(x)= sqrt(9-x^2)

[spice ingot]

But how can this possibly

Yield

0

[shadow comet]

if x=3

or x=-3

💀

[spice ingot]

Oh

Yeah sqr of 0 is 0

[shadow comet]

yea

so

[spice ingot]

I thought it would be error

Nice

Tysm

[shadow comet]

ur welcome

[spice ingot]

WAIT

[shadow comet]

wut

[spice ingot]

if you can input any given value of x

Why can’t we do -4?

[shadow comet]

...

wut

try to input it

look at wut u get

it wouldnt even exist

wellll

it would

[spice ingot]

Error

[shadow comet]

but i dont think its ur level yet

[spice ingot]

Whatt

[shadow comet]

its ccalled complex numebrs

imaginary

uh

idk how to explain

[spice ingot]

How

It’s simply just a sign

[shadow comet]

but functions only output real solutions

think abt it

when inputing -4

u get

[spice ingot]

Can’t we re-iterate this

[shadow comet]

sqrt 9-16

sqrt-7

[spice ingot]

Just say 7

And add the symbol

Or negative

[shadow comet]

u cant just do that

[spice ingot]

At the end?

Why

[shadow comet]

-sqrt 7 doesnt equal

sqrt-7

well what sign

would sqrt -7 be

[spice ingot]

We treat the signs as magnitude that’s why?

How

Does that look like a circle

[shadow comet]

bro

ur not required to graph

[spice ingot]

LOLL

[shadow comet]

yeas

centered 0, 0

radius 3

[spice ingot]

Can you explain

Look

Lets say we have a positive number

[shadow comet]

ok?

[spice ingot]

That is above 1

When we square it

It becomes closer to 0

[shadow comet]

bro

[spice ingot]

Why cant squaring a negative number above negative 1

[shadow comet]

wait nvmd

[shadow comet]

because

[spice ingot]

Yield something close to 0

[shadow comet]

squares are always positives

like

when u have a positive number

square it

u get positive

when u have negative numebr

u square it

gives positivenumber

[spice ingot]

I meant square root

Lol

[shadow comet]

its just the opposite

squares cant be negative

[spice ingot]

Where are these numbers

I get error on my calc

[shadow comet]

on the complex plane

[shadow comet]

yea'

thats wht

why

[spice ingot]

Frog can you do the math

On a piece of paper

Square root of -3

[shadow comet]

there is no math to that 😭

[spice ingot]

LOLL

Someone has to make the math th

[shadow comet]

look

i'll give explanation on how

[spice ingot]

Frog just do sqr root of -3

Okay

[shadow comet]

BRO

there is none

[spice ingot]

OKOK

[shadow comet]

💀

[spice ingot]

i would say number 2 💀

[shadow comet]

@spice ingot

wut grade u in

[spice ingot]

Yes

12

[shadow comet]

12th
;11

;

?!?!!

[spice ingot]

Umm

Does square root of a negative number make no sense to you

[shadow comet]

ur in 12th grade?!?!

[spice ingot]

Yea

[shadow comet]

bro...

i think ur kinda screwed

if u dont know complex numbers

[spice ingot]

Why 💀

[shadow comet]

bc

[spice ingot]

What are complex numbs

[shadow comet]

they are numbers

that have i in them

where i is sqrt-1

so they are all numbers that exist

basically

[spice ingot]

Like real numbers

I.e: continuous numbers?

[shadow comet]

no

[spice ingot]

I don’t understand

[spice ingot]

What does this symbol do?

[shadow comet]

just search it up

this questions done

[spice ingot]

Its just a notation yea?

[shadow comet]

yea

[spice ingot]

Oh

But realistically we can’t square a number

That is

Neg

[shadow comet]

u can

but the square of a number

cant be neg

[spice ingot]

Even the base?

If we raise it to the

1/2 power

[shadow comet]

yea

u cant square root a negative number

[spice ingot]

I mean u cna

It will result in a positive

Cuz its like

Negative time negative

[shadow comet]

🤦‍♂️

i didnt say square

i said square root

[spice ingot]

Im trippin lol

[shadow comet]

$sqrt{-x}$

[spice ingot]

SQUARE root

I don’t get

[lilac jolt]

edwad

[shadow comet]

bro latex trippin

$\sqrt{-x}$

[spice ingot]

Yo man, fr

Edwad

— frog

[lilac jolt]

edwad

[spice ingot]

Man I really need to know this

[shadow comet]

look

[spice ingot]

Can you do

[shadow comet]

$\sqrt{-1}$

[lilac jolt]

edwad

[spice ingot]

-3^1/2

[shadow comet]

ok?

no

u cant

[spice ingot]

Should be a way tho

Fr

Can you event a way

Just for me

[shadow comet]

there isnt

u can only simplify it

with i

[spice ingot]

You know how diving by zero

Makes absolutely no sense

How can you say

The sqr root of a negative number

Makes no sense

[shadow comet]

because

[spice ingot]

By explaining it

[shadow comet]

bro just search it up

imaginary numbers for beginners

[spice ingot]

Wait

Where did u learn imminary numbers

[shadow comet]

im in 7th grade

idk

i just learned it ig

[spice ingot]

Oh

DAMM

Edward bro

Tbh

U need to make

The square root Of a negative

Numb

Just for me

[neon spire]

are you all still talking about finding the domain and range of x^2+y^2=9?

[spice ingot]

Yea, kinda

[shadow comet]

no

well igtg

[neon spire]

alright

[spice ingot]

And then we got into negative square roots

[shadow comet]

i need to go slep

[spice ingot]

Edward’s tryna help me square root

The negative number

Of 7

We’re making progress

[neon spire]

where is it?

[spice ingot]

Srry, what

[neon spire]

ah nvm
you're just talking about sqrt(-7)?

[spice ingot]

Yea

You can simply just put a negative on the outside of this

Its like the sqr root of a negative numb no?

[neon spire]

right?

[spice ingot]

Is that the sqr root of a negative number

That’s what im saying

Wait no

[neon spire]

where's the square root?

[spice ingot]

Nvm that would be a negative exponent

Square root it so weird

I understand 2^2 is 2x2 or a number times itself a certain number of times

What the heck does a fraction of that mean?

[neon spire]

the exponent is still positive
it's still 2

[spice ingot]

No like I meant it represents x^-2

[neon spire]

yeah

[spice ingot]

How bout this

[neon spire]

it's a root

a^(m/n) is the nth root of a^m

[spice ingot]

How do you type it like 2^2= 2x2

But 2^1/2 = what the heck is going on here

[neon spire]

that's the square root of 2

[neon spire]

oh wait

[neon spire]

haha whoops

[spice ingot]

Lol

Ok lemme try

3^2/1

Got 9 yea

LOL IDK what im doing

Hmm

Wth

[spice ingot]

why is square root not the number divide by itself a number of times

Its directly the opposite of what’s happening no?

[neon spire]

hmm i'm not sure why people decided it should be that

probably something like this:

[neon spire]

and i guess the only thing which satisfies that is the square root of a

[spice ingot]

What do you think of square roots as?

[neon spire]

the square root of a number is just some other number which when multiplied by itself, returns the original number

[spice ingot]

O

And then log is the exponent of that ideal number? To the nth order

[neon spire]

a log is just the opposite of an exponent really

[spice ingot]

Kinda yea

Srry

On my calculator

I’m not sure how to

Enter the base and total value

Of the log function

[spice ingot]

WHAT

[neon spire]

wait

this is what happens when i'm in 2 conversations at once lmao

[neon spire]

🤦‍♂️

[spice ingot]

Loll

How do I do this on my calc?

[neon spire]

i don't think you can on that calculator

a lot of scientific calculators don't have log_b(a)

[spice ingot]

Whatt

Why won’t they code that in Lol

[neon spire]

no idea

[spice ingot]

How the heck

Do computers

Do

Square root

Of numbers

[neon spire]

hmm

newton's method maybe?

[spice ingot]

Isn’t so hard to do by yourself

[neon spire]

ok nvm

[spice ingot]

Like the square root of 5

[neon spire]

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

[pallid grove]

was this solved

[spice ingot]

Yes

[glad vessel]

.solved