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 |

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download