How do you w rite
in te r v a l n o ta tio n as
an inequality?
It may help to read its
meaning aloud first.
[-4 , 6 ) means all real
num bers g re a te r th a n
o r equal to - 4 and less
than 6.
You can use an inequality such as x ^ - 3 to describe a p o rtio n of th e n u m b e r line
called a n interval. You can also u se interval notation to describe an interval on th e
number line. In te rv a l n o ta tio n includes th e u se of th ree special symbols. These
sym bols include
parentheses: Use (or) w h en a < or > symbol indicates th a t th e interval's endpoints
are not included.
brackets: Use [ or ] w h e n a ^ or > symbol indicates th a t th e interval’s endpoints
are i n c l u d e d.
infinity: Use °° w h en th e interval co n tin u es forever in a positive direction.
Use - oo w h en th e interval co n tin u es forever in a negative directio n.
Inequality
x> 2
x< 2
1 < x s 5
x<-3 orr>4
Gr ap h
H h
-3 -2 -1
*—I----- 1 b
-3 -2 -1
H ©----1-
H 1-
-1
H h
-I—►
-6 -4 -2
Int erval Notation
[2; °°)
(-00,2)
(1,5]
(- 00 , - 3 ) or [ 4 ,oo)
(IIe SSD Using Interval Notation
Q What is the graph of [ —4 , 6 )? How do you write [ —4 , 6 ) as an inequality?
The bracket indicates th a t
- 4 is included. So use a
closed circle a t - 4.
The parenthesis indicates
that 6 is not included. So
use an open circle a t 6.
Shade between
-4 and 6.
The inequality - 4 ^ x < 6 rep resen ts th e interval n o tatio n [ - 4 , 6).
O What is the graph of x ^ — 1 o r x > 21 How do you write x ^ — 1 or .r > 2 in
interval notation?
I I " H---- 0 —H----b
-4 -3 -2 -1 0 1 2 3 4
The interval n o tatio n ( - oo, - 1] or (2, oo) rep resen ts th e inequality r<-lorx>2.
G o t It? 5. a. W hat is th e graph of (—2, 7]? How do you w rite (—2,7] as a n inequality?
b. W hat is th e graph of y > 71 How do you w rite y > 7 in interval notation?
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