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- kohai

Domain and range looking at graphs

- hwyl

oh okay
go on

- kohai

There is nothing to go on v,v I don't know how to do it

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## More answers

- kohai

Omg satellite don't make fun of me ;-;

- hwyl

oh okay
we have
domain
co-domain
range
do you know each of those?

- kohai

I saw that >.<

- anonymous

i wasn't

- anonymous

i was laughing at @hwyl

- kohai

I know that domain is the x-values and range is the y. I can do it based off of coordinates but I can't do it based off of graphs

- hwyl

oh okay
that's fine create a graph for me do not label

- anonymous

|dw:1443148507651:dw|

- kohai

It's mostly the unlabled infinity graphs I have issues with

- hwyl

just when I said do not label -_-

- hwyl

let us do an example based off your book

- kohai

|dw:1443148694480:dw|
Start with an easy cubic

- hwyl

okay

- hwyl

we're going to use the most basic cube function \(f(x) = x^3 \)

- kohai

Sure

- hwyl

so what is the domain of the function?

- kohai

\[(-\infty, \infty)\] ?

- hwyl

this is when you try to think about the pretty set-builder notation or that

- hwyl

can x be any number?

- kohai

I think so yeah

- hwyl

think hard, what condition that it won't work

- kohai

I feel really stupid for not knowing =.=

- hwyl

we have Real numbers etc etc

- kohai

Imaginary numbers? So like i and stuff I guess

- hwyl

aha! there you go

- anonymous

|dw:1443149075246:dw|

- kohai

Yeah, the solid lines like that I'm okay with. It's stuff that I don't see an end to like parabolas and cubic graphs etc

- hwyl

so pretty much any real number is valid

- anonymous

|dw:1443149216613:dw|

- Cookie_2046

https://www.youtube.com/watch?v=wu5iAgJ65dA

- kohai

@satellite73 , R=all real numbers?

- kohai

This is where I start getting lost haha

- hwyl

|dw:1443149291544:dw|

- hwyl

since you were talking about infinities, let us try something periodic with infinity

- hwyl

just pardon my drawing

- kohai

You're pardoned ;)

- hwyl

it's basically a graph of \(tan(x) \)

- hwyl

suppose the domain, co-domain and range

- hwyl

oops yes that!

- hwyl

went too happy with the vertical lines

- hwyl

|dw:1443149631927:dw|

- hwyl

|dw:1443149780293:dw|

- kohai

Pretty drawings

- hwyl

let us see what the domain, range and period

- kohai

I don't need to know period or co-domain. It's alg2 level rn

- hwyl

oh so what is the domain and range?

- kohai

domain [-pi/2, pi/2] range (-inf, inf)

- hwyl

okay now think carefully
does the x really cross or touch +/- pi/2

- kohai

No

- hwyl

so you can't really say \( \pm\pi/2 \)

- hwyl

maybe we can suppose that it is \(x \neq \pm \pi/2\)

- kohai

v,v I won't have super complex domains and ranges on this test though

- hwyl

oh okay then let us make it easier
how about sin x
draw the graph and indicate the domain and range

- kohai

|dw:1443150342371:dw|

- hwyl

make it a little smaller

- kohai

Please tell me thats a sin graph...

- kohai

ur jelly of my drawing skills

- kohai

|dw:1443150458901:dw|

- hwyl

|dw:1443150441508:dw|

- hwyl

|dw:1443150577160:dw|

- hwyl

indicate your domain and range

- kohai

Domain [0, inf)
Range [1, -1]

- hwyl

|dw:1443150722246:dw|

- kohai

Oh.
(-inf, inf)

- hwyl

yes, because there is no constraint in the value of x provided that we use Real number

- hwyl

@iambatman we need to do polarization later

- hwyl

always from left to right or least to most
so negative to positive

- kohai

Gotcha, okay

- hwyl

you pretty much get it already

- kohai

Yeah I guess so. I just have to think about them. I can do linear because I can physically see, stuff with infinity is a bit more abstract

- hwyl

|dw:1443151574827:dw|

- hwyl

what is your domain and what is your range?

- kohai

For some reason this puzzles me ;-;

- hwyl

alright start with range

- kohai

That's the part that's confusing me....... this is stupid v,v lol

- hwyl

|dw:1443151869375:dw|

- hwyl

can my range go lower than a?

- kohai

No

- hwyl

so there you go, you start with that value
range:[1, inf)

- kohai

Oh I guess that makes sense. I got the 1 but I wasn't sure about the second coordinate

- hwyl

I mean range:[a, inf)

- hwyl

pellet, I was going to ask you about the one with the detailed function

- hwyl

instead of an actual number, I assigned a

- kohai

Lol

- hwyl

but they are the same
|dw:1443152138070:dw||dw:1443152147095:dw|

- hwyl

you said earlier that domain is x and range is y
|dw:1443152218860:dw|

- hwyl

these are specific domains x, which gives you a range |dw:1443152497889:dw|

- kohai

Gotcha

- hwyl

but see, no matter what values you have for x, your y can only go up from 1

- kohai

Hey I appreciate you helping me :)

- hwyl

that's why our range starts from 1 to infinity

- hwyl

that is because how the function is set up, constrained by the constant k |dw:1443152666861:dw|

- hwyl

do you want me to get a few sample problems from a book?

- kohai

Nah, I think I've got it. And even if I get like the 2 problems with domain and range wrong I know the rest of the stuff lol. I think I'll be fine. Thank you for helping me :)

- hwyl

okay that's from a graph, how about from a function or equation?

- kohai

Those I can do fine

- kohai

And I'm starting to not process stuff lol. I think I'm good for now

- hwyl

\(\large f(x) = \frac{1}{x^2-4} \)

- hwyl

can you write your domain in set-builder notation?

- kohai

Mehhh lemme look at some examples and come back to this

- hwyl

wowwwww lol
alright, I need to grab something to eat

- kohai

I can't remember how to do it lol

- hwyl

oh, you just need to remember the definition of a function

- kohai

The y-coordinates can be the same, there just can't be more than one x-coordinate

- hwyl

so your domain basically anything that the denominator will not be zero

- kohai

So it can't be 2 or -2

- hwyl

\(x^2 + 4 = 0 \)
solve for x

- hwyl

correct, so all real except for those two

- kohai

How do I do that with notation?

- hwyl

try

- kohai

(-inf, -2] u [-2, 2] u [2, inf)

- hwyl

\(x|x~ \epsilon~ \mathbb{R}, x \neq \pm 2 \)

- kohai

I think my teacher wants me to use that stupid u thing

- hwyl

it is time for you to master it

- hwyl

between pre-cal and cal, there's usually a program that helps you hone skills on logic and these notations

- hwyl

inquire about it in your math department
it will help a lot

- kohai

Will do

- hwyl

okay let us attempt to drive this home

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