Download Interval Notation

Inclusive  [ ]  equal to 
Exclusive  ( )  not equal 
Left
(small)
2 x 3
x4
2 x
All Real Numbers
All Real Numbers except 1
Right
(big)
[-2,
(-2,
3]
∞)
(-∞,
4)
(-∞ , (-∞
1)
U,∞)
(1, ∞)
Union (U) means or. So we are
It goes
left to,
forever
right
choosing
everything
negative
Infinity
and
negative
Equal
usefrom
[and
] infinity
forever,
it’s
negative
infinity
up toso1,with
and
are
always
(then
). from 1 to
Not
to,we
useare
( ) taking out
infinity
toequal
the But
left,
positive
positive
infinity.
Since
goes
left
forever,
we circle
infinity
to
the
right.
one.
It’s itlike
if we
have
an open
negative
infinity.
on use
a number
line.
0
Basic Domains
1
x 1
Denominator cannot equal
zero.
x 1  0
x  1
All quantities inside square
roots must be greater than or
equal to zero.
So x  1
All other x' s work, so
the domain is all real
To find where the
denominator can’t be zero,
make it equal zero and solve.
numbers except - 1
D: (-∞ , -1) U (-1, ∞)
0
Basic Domains
4 x
Denominator cannot equal
zero.
4 x  0
x x
All quantities inside square
roots must be greater than or
equal to zero.
4 x
Make quantity inside square
root bigger than or equal to
zero and solve.
D: (-∞ , 4]
0
f
Find the domain of
g
remember, denominato r
can' t equal 0
1) Find the domains of each
2) Find where they overlap
f ( x)  4  x
4 x  0
g ( x)  x 2  4
(,)
x x
4 x
( ,4]
3) Find where denominator
equals zero.
4) Write the domain, a number
line may help.
We are taking out -2 and 2.
D:2)(-∞
, 4]4]
D: (-∞ , -2) U (-2,
U (2,
0
x2  4  0
x  2
f
Find the domain of
g
remember, denominato r
can' t equal 0
1) Find the domains of each
2) Find where they overlap
f ( x)  4  x
4 x  0
g ( x)  x  1
x 1  0
x x
4 x
( ,4]
1 1
x 1
[1, )
3) Find where denominator
equals zero.
4) Write the domain, a number
line may help.
You don’t want to change it to 2 on the
left. Look at the number line, by
changing it to 2, it’s not the same.
We are taking out 1
D: (1,
[1 , 4]
4]
0
x 1  0
x 1