Algebra 2 H/GT
Interval Notation Notes and worksheet
Set Builder Notation
x | x  a
x | x  a
x | x  a
x | x  a
x | a  x  b
x | a  x  b
x | a  x  b
x | a  x  b
All reals
Interval
Notation
 a,  
a, 
 , a 
 , a
 a, b 
a, b
 a, b 
 a, b 
 ,  
We use the union symbol (  ) to represent the word or.
For example x | x  3 or x  4 would be written as  ,3   4,   .
Note: we always use soft brackets for infinity, never hard brackets.
Examples: Write the domain and range in interval notation
D:  6,  
D:  ,3   3,  
D:  4, 1   1, 2   2,5
R:  ,3
R:  , 4
R:  3,0   0,1
Assignment: Answer the following on you own notebook paper.
I. Given the following in set-builder notation, express the answer in interval notation.
1. { x | x  4 or x  6 }
2.  x | 5  x  7
3. x is all reals
II. Given the following in interval notation, express the answer in set-builder notation.
5. ( –  , 4]
6. ( –  , – 3 ] ( 4 ,  )
7. [ 2 , 6 )
4.  x | x   5
8. ( 5 , 8)
III. For each graph, describe the domain and range using interval notation. Determine if the graph is a function.
9.
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