Transcript Interval Notation

Inclusive  [ ]  equal to 
Exclusive  ( )  not equal 
Left
(small)
Right
(big)
2 x 3
x4
2 x
[-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
All Real Numbers
forever,
it’s
negative
infinity
up toso1,with
and
are
always
(then
). from 1 to
Not
to,we
useare
( ) taking out
All Real Numbers except 1 positive
infinity
toequal
the But
left,
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
numbers except - 1
To find where the
denominator can’t be zero,
make it equal zero and solve.
D: (-∞ , -1) U (-1, ∞)
0
Basic Domains
4 x
Denominator cannot equal
zero.
4 x  0
x x
4 x
All quantities inside square
roots must be greater than or
equal to zero.
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