Matt Wolf



Domain - the set of all x-values for which a function is defined

Range - the set of all y-values for which a function is defined

To Define the Domain of a Function (Algebraically)

Interval Notation

Open Brackets: ( , ) means endpoints are not included in the set

Closed Brackets: [ , ] means endpoints are included in the set

Mixed Brackets 1: ( , ] means minimum is not included; maximum is included

Mixed Brackets 2: [ , ) means minimum is included; maximum is not included

|Example |Set |Interval Notation |

|[pic] |All x-values less than 5 not including 5 |(-∞, 5) |

|[pic] |All x-values less than and including 5 |(-∞, 5] |

|[pic] |All x-values between (but not including) 0 and 5 |(0, 5) |

|[pic] |All x-values between 0 and 5 including 0 |[0, 5) |

To Define the Domain and Range of a Function (Graphically)

• To define the domain, read the graph from left (-∞) to right (∞) along the x-axis. Use interval notation beginning with the first x-value that is defined for the graph.

• To define the range, read the graph from bottom (-∞) to top (∞) along the y-axis. Use interval notation beginning with the first y-value that is defined for the graph.

• Any holes (open circles) or parts of the graph without x or y-values (gaps) are not in the domain or range of the function.

Example: Examine Graph A. Our goal is to define the domain and range of Graph A. To accomplish this task, examine Graph B and read the graph along the x-axis to define the domain. Examine Graph C and read the graph along the y-axis to define the range.

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Case 1: Polynomial Case 2: Fraction Case 3: Square Root

[pic] [pic] [pic]

Graph A Graph B Graph C

[pic] [pic] [pic]

Domain: ___________________ Range: ____________________

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