Name
Name: ____________________________ Date: _____________________ Period: _____
Introduction to Interval and Set Builder Notation
Set Builder Notation – A formal way of describing a set of number values on the same line.
Notation: { x | -5 ≤ x ≤ 1 }
Read: “x such that negative five is less than or equal to x which is less than or equal to one.”
Visual:
_________________________________________________________________________
Notation: { x | x ≤ -8 or x > 0 }
Read: “x such that x is less than or equal to negative eight or x is greater than zero.”
Visual:
_________________________________________________________________
Interval Notation – Notation for representing an interval as a pair of number. The numbers are the endpoints of the interval. Parenthesis, ( or ), and/or brackets, [ or ], are used to show whether the end points are included or not.
Notation: x is in [-5, 1]
Read: “x in the interval from and including negative five to and included one.”
Visual:
________________________________________________________________________
Notation: x in (-∞, -8] U (0, ∞)
Read: “x in the interval from negative infinity to and including negative eight or from and excluding zero to positive infinity.”
Visual:
Directions: Write the interval and set builder notations for each number line graph given.
|Interval Notation |Set Builder Notation |Number Line Graph |
| | |[pic] |
| | |[pic] |
| | |[pic] |
| | |[pic] |
| | |[pic] |
| | |[pic] |
| | | |
| | | |
|[pic] |[pic] |[pic] |
|Interval Notation|Set Builder Notation |Interval Notation |Set Builder Notation |Interval Notation |Set Builder Notation |
| | | | | | |
Name: ____________________________ Date: _____________________ Period: _____
Practice: Interval & Set Builder Notation
Objective: The student will apply knowledge of interval and set builder notation to graphing and interpreting number line graphs.
| |Set Builder Notation |Interval Notation |Number Line Graph |
|Ex. |{x|[pic]} |[- 3, 5) | |
| | | | |
|Ex |{x|[pic]} |(2, () | |
| | | | |
|1. |{x|[pic]} | | |
| | | | |
|2. | |(-(, 4) | |
| | | | |
|3. | | | |
| | | | |
|4. | |[5, () | |
| | | | |
|5. |{x|[pic]or[pic]} | | |
| | | | |
|[pic] |[pic] |[pic] |
|Interval Notation |Set Builder Notation |Interval Notation |Set Builder Notation |Interval Notation |Set Builder Notation |
| | | | |y in | |
| | | |{y | -2 < y ≤ 3 } |[-2, 1] U (3,∞) | |
Name: ____________________________ Date: _____________________ Period: _____
Check for understanding – Interval and Set Builder Notation
| |Set Builder Notation |Interval Notation |Graph |
|1. |{x |[pic]} | | |
| | | | |
|2. | | | |
| | | | |
|3. | |(–∞, 2][pic](5,[pic]) | |
| | | | |
Name: ____________________________ Date: _____________________ Period: _____
Check for understanding – Interval and Set Builder Notation
| |Set Builder Notation |Interval Notation |Graph |
|1. |{x |[pic]} | | |
| | | | |
|2. | | | |
| | | | |
|3. | |(–∞, 2][pic](5,[pic]) | |
| | | | |
Name: ____________________________ Date: _____________________ Period: _____
Check for understanding – Interval and Set Builder Notation
| |Set Builder Notation |Interval Notation |Graph |
|1. |{x |[pic]} | | |
| | | | |
|2. | | | |
| | | | |
|3. | |(–∞, 2][pic](5,[pic]) | |
| | | | |
Name: ____________________________ Date: _____________________ Period: _____
Homework Assignment – Intervals, Domain, and Range DUE DATE: __________
Complete each row of the table below by using the information or number line graph given.
| |Set Builder Notation |Interval Notation |Number Line Graph |
|1. | | | |
| | | | |
|2. |{x|[pic] all real numbers}| | |
| | | | |
|3. | | | |
| | | | |
|4. | |(1, 4) | |
| | | | |
|5. |{x|[pic]} | | |
| | | | |
|6. | |[-2, 2] | |
| | | | |
7. 8. 9.
|[pic] |[pic] |[pic] |
|Interval Notation |Set Builder Notation |Interval Notation |Set Builder Notation |Interval Notation |Set Builder Notation |
| | | | |y in | |
| | | |{y | -∞ < y ≤ 3 } |(0, 1] U (4,∞) | |
10. 11.
Domain: Domain:
Interval ______________________ Interval ______________________
Inequality ______________________ Inequality ______________________
Range: Range:
Interval ______________________ Interval ______________________
Inequality ______________________ Inequality ______________________
12. 13.
Domain: Domain:
Interval ______________________ Interval ______________________
Inequality ______________________ Inequality ______________________
Range: Range:
Interval ______________________ Interval ______________________
Inequality ______________________ Inequality ______________________
Name: ____________________________ Date: _____________________ Period: _____
Describing a Graph
Objectives:
• The student will analyze a graph and describe components of a piece-wise graph verbally using formal vocabulary.
• The student will use interval notation to describe changes and functional values of a graph.
1. Describe what is happening in the graph to the right. Use the word bank to help you in your description.
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
Apply what you know: Let the graph above be called f(x). Answer the following questions:
2. On what intervals of x is f(x) increasing?
3. On what intervals of x is f(x) positive?
4. On what intervals of x is f(x) decreasing?
5. On what intervals of x is f(x) constant?
6. On what intervals of x is f(x) negative?
Additional Practice
| | |[pic] |
| | |[pic] |
| | |[pic] |
| | |[pic] |
-----------------------
[pic]
[pic]
[pic]
[pic]
-4
-3
-2
-1
0
1
2
3
4
6
5
-4
-3
-2
-1
0
1
2
3
4
6
5
-4
-3
-2
-1
0
1
2
3
4
6
5
-4
-3
-2
-1
0
1
2
3
4
6
5
-4
-3
-2
-1
0
1
2
3
4
6
5
8
-2
-1
0
1
2
3
4
5
6
7
-4
-3
-2
-1
0
1
2
3
4
6
5
-4
-3
-2
-1
0
1
2
3
4
6
5
-4
-3
-2
-1
0
1
2
3
4
6
5
-4
-3
-2
-1
0
1
2
3
4
6
5
-4
-3
-2
-1
0
1
2
3
4
6
5
-4
-3
-2
-1
0
1
2
3
4
6
5
-4
-3
-2
-1
0
1
2
3
4
6
5
-4
-3
-2
-1
0
1
2
3
4
6
5
4
-6
-5
-4
-3
-2
-1
0
1
2
3
-4
-3
-2
-1
0
1
2
3
4
6
5
x
y
O
2
2
x
y
O
2
2
x
y
O
2
2
x
y
O
2
2
|slope |x-intercept |y-intercept |
|positive |increasing |decreasing |
|function |negative |constant |
|minimum |linear |maximum |
|domain |rate of change |range |
................
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