Whats the trick for knowing which ( ) or [ ] go where in interval notation?

- Destinyyyy

Whats the trick for knowing which ( ) or [ ] go where in interval notation?

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- jamiebookeater

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- Destinyyyy

Like...
(- infinity sign, infinity sign)
(- infinity sign, -1]
(-3,0]
[-1,8)

- BishopPatton

Let's draw a number line with these four special numbers marked:
-x <------o----o----o----o----0----o----o----o----o------> +x
-3 -1 1 3
The trick is to look at the sign (+ or -) of your expression in each
one of the intervals where nothing changes sign from + to - or back.
These intervals are "up to but not including -3", "strictly between
-3 and -1", etc. There are 5 of them.
As an example, let's see what happens between -1 and +1. The numerator
has one positive factor and one negative factor. The same is true for
the denominator. So both numerator and denominator are negative,
making the fraction > 0.
Now we know that it is >= 0 in the interval (-1,+1). Remember the
fraction is 0 for x=-1 and undefined for +1, so we write [-1,+1); the
square cornered bracket on the left shows -1 IS IN the interval we are
talking about where the fraction is >= zero. With me so far?
Now do this kind of analysis about the 4 other sub-intervals to see
what happens. As for the graph for such a problem, just draw on the
number line to show what x values are included. There are two ways to
show that an end point is or isn't included in the graph. Some books
use "[" and "(" for this and some use a filled-dot and hollow-dot for
it. Look in your book.
I hope this helps.

- BishopPatton

i am tired as heck after having to type that lol

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## More answers

- BishopPatton

Please medal and fan if this helps you

- welshfella

note when one of the numbers infinity or - infinity it's always a '(' or ')'

- BishopPatton

Yep

- Destinyyyy

Um what?

- Destinyyyy

I have no clue what dot things your talking about. I dont have a book to look at

- BishopPatton

if you read everything outloud to yourself it will make sense

- Destinyyyy

My examples show ( ) and [ ]

- BishopPatton

That is all i can do to help. i hope you understand

- Destinyyyy

I rather no draw a number line for every problem I do.. Is there a easier way

- Destinyyyy

not *

- Destinyyyy

It doesnt matter if I read it allowed or not I dont understand anything you said.

- welshfella

one of your examples is (-3,0]
that means 'greater than -3 and less than and including 0'.

- Destinyyyy

Okay I get that.. And my examples were just to show someone what Im talking about

- welshfella

so are you happy with the answers given?

- Destinyyyy

Um not really.. Im still where I was before.. Can you maybe give me an example to solve or something? Im working with domain and range right now

- welshfella

ok
so what does
[ , INf sign) mean

- Destinyyyy

? Like [1, infinity sign) ??

- welshfella

yes

- Destinyyyy

Okay.. [ means less than and including 1.. ) means greater than infinity

- welshfella

No It means greater than and including 1 and up to infinity

- Destinyyyy

I dont get it then

- welshfella

- in other words all numbers from and including 1 and going on infinaiely

- welshfella

well try an easy one
{3 , 6)
this is all numbers greater than and including 3 and less than 6
the [ means that 3 is included and the ) at the end means 6 is NOT included

- welshfella

that the square bracket [

- welshfella

means 'included'

- Destinyyyy

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- welshfella

also its important to remember that its a continuum of numbers between these to values not just 4 and 5 its 3.9011, 5.5 , 5.9999 and whatever

- Destinyyyy

This is what im working on. I really understand what you just said. Im trying to but its not making any sense to me

- Destinyyyy

I dont care about that. I just want to know how to know where to put () and []

- Destinyyyy

I assumed there was some trick people knew that helped them figure it out quick.

- triciaal

when you have square it includes the end values

- welshfella

the domain is all the values of x that the function can take
the empty circle means that that values of x is not included and the filled means that values of x is included.

- Destinyyyy

Yes..

- welshfella

yes
the domain for that function is
(-3,0]

- welshfella

the x -3 has the emplty circle but x = 0 has filled one

- Destinyyyy

Yeah.. But how do you know where to put the 9 and ] at??

- Destinyyyy

( ] **

- welshfella

well ( when the number is not included - so it comes before the -3

- welshfella

|dw:1441818059986:dw|

- Destinyyyy

Um okay I think I understand that..

- Destinyyyy

So the range would be (5,-4] ??

- welshfella

the lowest value of y comes first in the range
this is -5
and the highest is 5

- welshfella

Sorry lowest is -4

- Destinyyyy

So [-4,5)

- welshfella

yes

- welshfella

-4 is included but 5 is not

- Destinyyyy

Okay I think I understand

- welshfella

good

- Destinyyyy

Thank you.

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