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4.6 – Formalizing Relations and Functions

4.6 – Formalizing Relations and Functions. Vocab, Vocab, Vocab!!. Relation – a pairing of numbers in one set with numbers in another set. Domain – the set of x-values of a relation Range – the set of y-values of a relation.

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4.6 – Formalizing Relations and Functions

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  1. 4.6 – Formalizing Relations and Functions

  2. Vocab, Vocab, Vocab!! • Relation – a pairing of numbers in one set with numbers in another set. • Domain – the set of x-values of a relation • Range – the set of y-values of a relation

  3. 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: {-2, 0, 4, 5} RANGE: {0.5, 2.5, 6.5} Domain Range -2 0 4 5 0.5 2.5 6.5 Yes, the relation is a function because each domain value is mapped to one range value.

  4. 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 DOMAIN: {4, 5, 6} RANGE: {3, 4, 5, 8} 3 4 5 8 4 5 6 No, the relation is not a function because the domain value 6 is mapped to two range values.

  5. And more vocab! 4. Vertical Line Test – another way to decide if a relation is a function. If a vertical line crosses a graph only once, then the relation is a function If a vertical line crosses a graph more than once, then the relation is not a function.

  6. Are the following relations functions? Use the vertical line test.

  7. Just one more vocab word! 5. Function Notation: replacing y with f(x) in an equation that represents a function. Example: f(x) = -3x + 1

  8. Find the range for each function for the given domain. • f(x) = 5x – 2; {-1, 3, 10} • f(x) = |x – 2|; {-3, 0, 4}

  9. Homework Page 272 # 8 – 15, 18 – 21, 24 - 25

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