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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