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§4.6 Formalizing Relations and Functions

§4.6 Formalizing Relations and Functions. Example 1 : Identifying Functions Using Mapping Diagrams. Identify the domain and range of each relation. Represent the relation with a mapping diagram. Is the relation a function? {(-2, 0.5), (0, 2.5), (4, 6.5), (5, 2.5)}. Domain. Range.

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§4.6 Formalizing Relations and Functions

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  1. §4.6 Formalizing Relations and Functions

  2. Example 1: Identifying Functions Using Mapping Diagrams • Identify the domain and range of each relation. Represent the relation with a mapping diagram. Is the relation a function? • {(-2, 0.5), (0, 2.5), (4, 6.5), (5, 2.5)} Domain Range Each domain value is mapped to ONLY ONE range value. The relation IS a function. -2 0 4 5 0.5 2.5 6.5

  3. Example 1: Identifying Functions Using Mapping Diagrams • Identify the domain and range of each relation. Represent the relation with a mapping diagram. Is the relation a function? • {(6, 5), (4, 3), (6, 4), (5, 8)} Domain Range The domain value 6 is mapped to 2 range values. The relation IS NOT a function. 4 5 6 3 4 5 8

  4. Example 2: Identifying Functions Using the Vertical Line Test • Is the relation a function? Use the vertical line test. {(6, 5), (4, 3), (6, 4), (5, 8)} The domain value 6 corresponds to 2 range values. The relation IS NOT a function.

  5. Example 2: Identifying Functions Using the Vertical Line Test • Is the relation a function? Use the vertical line test. f(x) = -1/3x2 + 3 There is no vertical line that passes through more than one point. The relation IS a function.

  6. Example 3: Evaluating a Function • The function w(x) = 250x represents the number of words w(x) you can read in x minutes. How many words can you read in 8min? • w(x) = 250x • w(8) = 250(8) • w(8) = 2000 You can read 2000 words per minute.

  7. Assignment: Pg. 271-272 8-23 Left

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