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**Function: Domain and Range**

Recall the definition of a function. A function is a correspondence from a first set, called the domain, to a second set, called the range, such that each element in the domain corresponds to exactly one element in the range. The first set is called the domain of the function. The second set is called the range of the function.

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**Function: Domain and Range**

In this course the members of each set are real numbers. For now, x will represent a real number from the domain and y or f (x) will represent a real number from the range. The following examples show how to find the domain and range from various function representations.

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**Function: Identifying the Domain and Range**

Example 1 (Function represented by a set of ordered pairs.) State the domain and range of the function: { (- 1, 2), (3, 5), (6, 5) }. The domain is { - 1, 3, 6 }, because each first set (domain) member is represented by x (the left slot in each ordered pair. The range is { 2, 5 }because each second set (range) member is represented by y (the second slot in each ordered pair.

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**Function: Identifying the Domain from an Equation**

Example 2: State the domain of Recall from the definition that each member of the domain must correspond to exactly one member of the range. Here, any number we choose to replace for x will result in exactly one value for y, except for x = 3.

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**Function: Identifying the Domain from an Equation**

Example 2: State the domain of This value of 3 for x does not correspond to a value for y, since, is not defined. Therefore, the domain is all real numbers except 3, or (- , 3) (3, ). Slide 3

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**Function: Identifying the Domain from an Equation**

Example 3: State the domain of Recall from the definition that each member of the domain must correspond to exactly one member (a real number) of the range. Here, only values of x that are - 3 or larger will correspond to a real number for y.

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**Function: Identifying the Domain from an Equation**

Example 3: State the domain of For example, if x = - 7, which is not a real number. One way to quickly find the domain is to set the radicand of an even index radical 0 and solve. Here, x 0, so the domain is x - 3 or [- 3, ).

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**Function: Identifying the Domain and Range from a Graph**

Example 4: State the domain and range of the graphed function. Note that points on the graph have x-coordinate values that span from - 4 to 4. Since each domain member is represented by x, the domain is [ - 4, 4 ]. Note that points on the graph have y-coordinate values that span from 0 to 5. Since each range member is represented by y, the range is [ 0, 5 ].

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**Function: Domain and Range**

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Chapter 1 A Beginning Library of Elementary Functions

Chapter 1 A Beginning Library of Elementary Functions

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