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Objectives

Learn to analyze relationships between values, identify domains and ranges, and determine if a relation is a function. Practice mappings and sets to represent relations effectively.

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Objectives

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  1. Objectives 2c) Analyze the relationship between x and y values, determine whether a relation is a function, and identify domain and range. (DOK 2)The student will be able to: • 1. identify the domain and range of a relation. • show relations as sets and mappings. Designed by Skip Tyler, Varina High School Adapted by Sarita Williams, Siwell Middle School

  2. Vocabulary The domain is the set of 1st coordinates of the ordered pairs. The range is the set of 2nd coordinates of the ordered pairs. A relation is a set of ordered pairs.

  3. Given the relation {(3,2), (1,6), (-2,0)}, find the domain and range. Domain = {3, 1, -2} Range = {2, 6, 0}

  4. The relation {(2,1), (-1,3), (0,4)} can be shown by x y 1) a table. 2) a mapping. 3) a graph. 2 -1 0 1 3 4 2 -1 0 1 3 4

  5. Given the following table, show the relation, domain, range, and mapping.x -1 0 4 7y 3 6 -1 3 Relation = {(-1,3), (0,6), (4,-1), (7,3)} Domain = {-1, 0, 4, 7} Range = {3, 6, -1, 3}

  6. Mappingx -1 0 4 7y 3 6 -1 3 You do not need to write 3 twice in the range! -1 0 4 7 3 6 -1

  7. Answer Now What is the domain of the relation{(2,1), (4,2), (3,3), (4,1)}? • {2, 3, 4, 4} • {1, 2, 3, 1} • {2, 3, 4} • {1, 2, 3} • {1, 2, 3, 4}

  8. Answer Now What is the range of the relation{(2,1), (4,2), (3,3), (4,1)}? • {2, 3, 4, 4} • {1, 2, 3, 1} • {2, 3, 4} • {1, 2, 3} • {1, 2, 3, 4}

  9. Give the domain and range of the relation. The domain value is all x-values from 1 through 5, inclusive. The range value is all y-values from 3 through 4, inclusive. Domain: 1 ≤ x ≤ 5 Range: 3 ≤ y ≤ 4

  10. Functions • A function is a special type of relation. A function is a relation in which each element of the domain is paired with exactly one element of the range. Another way of saying it is that there is one and only one output (y) with each input (x). y x f(x)

  11. 2 3 5 4 3 0 2 3 f(x) f(x) f(x) f(x) Determine whether each relation is a function. • {(2, 3), (3, 0), (5, 2), (4, 3)} • YES, every domain is different!

  12. Determine whether the relation is a function. 1 4 5 5 6 3 9 2 6 1 f(x) f(x) f(x) f(x) f(x) 2. {(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)} NO, 5 is paired with 2 numbers!

  13. Answer Now Is this relation a function?{(1,3), (2,3), (3,3)} • Yes • No

  14. Vertical Line Test (pencil test) If any vertical line passes through more than one point of the graph, then that relation is not a function. Are these functions? FUNCTION! FUNCTION! NOPE!

  15. Vertical Line Test FUNCTION! NO! NO WAY! FUNCTION!

  16. Give the domain and range of the relation. Tell whether the relation is a function. Explain. Draw in lines to see the domain and range values Range Domain D: –5 ≤ x ≤ 3 R: –2 ≤ y ≤ 1 The relation is not a function. Nearly all domain values have more than one range value.

  17. Answer Now Is this a graph of a function? • No • Yes

  18. A function is a special type of relation that pairs each domain value with exactly one range value. Function Notation Input Name of Function Output

  19. Given f(x) = 3x - 2, find: 1) f(3) 2) f(-2) = 7 3(3)-2 3 7 = -8 3(-2)-2 -2 -8

  20. Given h(z) = z2 - 4z + 9, find h(-3) (-3)2-4(-3)+9 -3 30 9 + 12 + 9 h(-3) = 30

  21. Answer Now Given g(x) = x2 – 2, find g(4) • 2 • 6 • 14 • 18

  22. Answer Now Given f(x) = 2x + 1, find-4[f(3) – f(1)] • -40 • -16 • -8 • 4

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