kohai
  • kohai
Mathematics
chestercat
  • chestercat
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kohai
  • kohai
Domain and range looking at graphs
hwyl
  • hwyl
oh okay go on
kohai
  • kohai
There is nothing to go on v,v I don't know how to do it

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kohai
  • kohai
Omg satellite don't make fun of me ;-;
hwyl
  • hwyl
oh okay we have domain co-domain range do you know each of those?
kohai
  • kohai
I saw that >.<
anonymous
  • anonymous
i wasn't
anonymous
  • anonymous
i was laughing at @hwyl
kohai
  • 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
  • hwyl
oh okay that's fine create a graph for me do not label
anonymous
  • anonymous
|dw:1443148507651:dw|
kohai
  • kohai
It's mostly the unlabled infinity graphs I have issues with
hwyl
  • hwyl
just when I said do not label -_-
hwyl
  • hwyl
let us do an example based off your book
kohai
  • kohai
|dw:1443148694480:dw| Start with an easy cubic
hwyl
  • hwyl
okay
hwyl
  • hwyl
we're going to use the most basic cube function \(f(x) = x^3 \)
kohai
  • kohai
Sure
hwyl
  • hwyl
so what is the domain of the function?
kohai
  • kohai
\[(-\infty, \infty)\] ?
hwyl
  • hwyl
this is when you try to think about the pretty set-builder notation or that
hwyl
  • hwyl
can x be any number?
kohai
  • kohai
I think so yeah
hwyl
  • hwyl
think hard, what condition that it won't work
kohai
  • kohai
I feel really stupid for not knowing =.=
hwyl
  • hwyl
we have Real numbers etc etc
kohai
  • kohai
Imaginary numbers? So like i and stuff I guess
hwyl
  • hwyl
aha! there you go
anonymous
  • anonymous
|dw:1443149075246:dw|
kohai
  • 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
  • hwyl
so pretty much any real number is valid
anonymous
  • anonymous
|dw:1443149216613:dw|
Cookie_2046
  • Cookie_2046
https://www.youtube.com/watch?v=wu5iAgJ65dA
kohai
  • kohai
@satellite73 , R=all real numbers?
kohai
  • kohai
This is where I start getting lost haha
hwyl
  • hwyl
|dw:1443149291544:dw|
hwyl
  • hwyl
since you were talking about infinities, let us try something periodic with infinity
hwyl
  • hwyl
just pardon my drawing
kohai
  • kohai
You're pardoned ;)
hwyl
  • hwyl
it's basically a graph of \(tan(x) \)
hwyl
  • hwyl
suppose the domain, co-domain and range
hwyl
  • hwyl
oops yes that!
hwyl
  • hwyl
went too happy with the vertical lines
hwyl
  • hwyl
|dw:1443149631927:dw|
hwyl
  • hwyl
|dw:1443149780293:dw|
kohai
  • kohai
Pretty drawings
hwyl
  • hwyl
let us see what the domain, range and period
kohai
  • kohai
I don't need to know period or co-domain. It's alg2 level rn
hwyl
  • hwyl
oh so what is the domain and range?
kohai
  • kohai
domain [-pi/2, pi/2] range (-inf, inf)
hwyl
  • hwyl
okay now think carefully does the x really cross or touch +/- pi/2
kohai
  • kohai
No
hwyl
  • hwyl
so you can't really say \( \pm\pi/2 \)
hwyl
  • hwyl
maybe we can suppose that it is \(x \neq \pm \pi/2\)
kohai
  • kohai
v,v I won't have super complex domains and ranges on this test though
hwyl
  • hwyl
oh okay then let us make it easier how about sin x draw the graph and indicate the domain and range
kohai
  • kohai
|dw:1443150342371:dw|
hwyl
  • hwyl
make it a little smaller
kohai
  • kohai
Please tell me thats a sin graph...
kohai
  • kohai
ur jelly of my drawing skills
kohai
  • kohai
|dw:1443150458901:dw|
hwyl
  • hwyl
|dw:1443150441508:dw|
hwyl
  • hwyl
|dw:1443150577160:dw|
hwyl
  • hwyl
indicate your domain and range
kohai
  • kohai
Domain [0, inf) Range [1, -1]
hwyl
  • hwyl
|dw:1443150722246:dw|
kohai
  • kohai
Oh. (-inf, inf)
hwyl
  • hwyl
yes, because there is no constraint in the value of x provided that we use Real number
hwyl
  • hwyl
@iambatman we need to do polarization later
hwyl
  • hwyl
always from left to right or least to most so negative to positive
kohai
  • kohai
Gotcha, okay
hwyl
  • hwyl
you pretty much get it already
kohai
  • 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
  • hwyl
|dw:1443151574827:dw|
hwyl
  • hwyl
what is your domain and what is your range?
kohai
  • kohai
For some reason this puzzles me ;-;
hwyl
  • hwyl
alright start with range
kohai
  • kohai
That's the part that's confusing me....... this is stupid v,v lol
hwyl
  • hwyl
|dw:1443151869375:dw|
hwyl
  • hwyl
can my range go lower than a?
kohai
  • kohai
No
hwyl
  • hwyl
so there you go, you start with that value range:[1, inf)
kohai
  • kohai
Oh I guess that makes sense. I got the 1 but I wasn't sure about the second coordinate
hwyl
  • hwyl
I mean range:[a, inf)
hwyl
  • hwyl
pellet, I was going to ask you about the one with the detailed function
hwyl
  • hwyl
instead of an actual number, I assigned a
kohai
  • kohai
Lol
hwyl
  • hwyl
but they are the same |dw:1443152138070:dw||dw:1443152147095:dw|
hwyl
  • hwyl
you said earlier that domain is x and range is y |dw:1443152218860:dw|
hwyl
  • hwyl
these are specific domains x, which gives you a range |dw:1443152497889:dw|
kohai
  • kohai
Gotcha
hwyl
  • hwyl
but see, no matter what values you have for x, your y can only go up from 1
kohai
  • kohai
Hey I appreciate you helping me :)
hwyl
  • hwyl
that's why our range starts from 1 to infinity
hwyl
  • hwyl
that is because how the function is set up, constrained by the constant k |dw:1443152666861:dw|
hwyl
  • hwyl
do you want me to get a few sample problems from a book?
kohai
  • 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
  • hwyl
okay that's from a graph, how about from a function or equation?
kohai
  • kohai
Those I can do fine
kohai
  • kohai
And I'm starting to not process stuff lol. I think I'm good for now
hwyl
  • hwyl
\(\large f(x) = \frac{1}{x^2-4} \)
hwyl
  • hwyl
can you write your domain in set-builder notation?
kohai
  • kohai
Mehhh lemme look at some examples and come back to this
hwyl
  • hwyl
wowwwww lol alright, I need to grab something to eat
kohai
  • kohai
I can't remember how to do it lol
hwyl
  • hwyl
oh, you just need to remember the definition of a function
kohai
  • kohai
The y-coordinates can be the same, there just can't be more than one x-coordinate
hwyl
  • hwyl
so your domain basically anything that the denominator will not be zero
kohai
  • kohai
So it can't be 2 or -2
hwyl
  • hwyl
\(x^2 + 4 = 0 \) solve for x
hwyl
  • hwyl
correct, so all real except for those two
kohai
  • kohai
How do I do that with notation?
hwyl
  • hwyl
try
kohai
  • kohai
(-inf, -2] u [-2, 2] u [2, inf)
hwyl
  • hwyl
\(x|x~ \epsilon~ \mathbb{R}, x \neq \pm 2 \)
kohai
  • kohai
I think my teacher wants me to use that stupid u thing
hwyl
  • hwyl
it is time for you to master it
hwyl
  • hwyl
between pre-cal and cal, there's usually a program that helps you hone skills on logic and these notations
hwyl
  • hwyl
inquire about it in your math department it will help a lot
kohai
  • kohai
Will do
hwyl
  • hwyl
okay let us attempt to drive this home

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