Question

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

Answer 1

Like...

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

Answer 2

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.

Answer 3

i am tired as heck after having to type that lol

Answer 4

Please medal and fan if this helps you

Answer 5

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

Answer 6

Yep

Answer 7

Um what?

Answer 8

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

Answer 9

if you read everything outloud to yourself it will make sense

Answer 10

My examples show ( ) and [ ]

Answer 11

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

Answer 12

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

Answer 13

not *

Answer 14

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

Answer 15

one of your examples is (-3,0]

that means 'greater than -3 and less than and including 0'.

Answer 16

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

Answer 17

so are you happy with the answers given?

Answer 18

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

Answer 19

ok
so what does
[ , INf sign) mean

Answer 20

? Like [1, infinity sign) ??

Answer 21

yes

Answer 22

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

Answer 23

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

Answer 24

I dont get it then

Answer 25

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

Answer 26

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

Answer 27

that the square bracket [

Answer 28

means 'included'

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

when you have square it includes the end values

Answer 34

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.

Answer 35

Yes..

Answer 36

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

Answer 37

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

Answer 38

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

Answer 39

( ] **

Answer 40

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