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Relationships in Mathematics

Learn how to find the value of x and y in various math equations, explore mapping diagrams, tables, graphs, and understand domains and ranges in relations and functions.

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Relationships in Mathematics

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  1. Find the value of y for each of the following values of x: #1 #2 #3 Find the value of x for each of the following values of y: #4 #5

  2. Find the value of y for each of the following values of x: #1

  3. Find the value of y for each of the following values of x: #1 #2

  4. Find the value of y for each of the following values of x: #1 #2 #3

  5. Find the value of x for each of the following values of y: #4 #5

  6. Find the value of x for each of the following values of y: #4 #5

  7. Find the value of y for each of the following values of x: #1 #2 #3 Find the value of x for each of the following values of y: #4 #5

  8. Table

  9. Table Ordered Pair

  10. Graph Y-axis Ordered Pair X-axis

  11. Vocabulary relation domain range function

  12. A relationship is a situation that can be described by a set of linked data. The data from a relationship can also be represented by a graph. Relationships can also be represented by a set of ordered pairs called arelation.

  13. Relationships can also be represented by a set of ordered pairs called arelation. For example: The scoring systems of a track meets is as follows: 1st place: 5 points 3rd place: 2 points 2nd place: 3 points 4th place: 1 point This scoring system is a relation, so it can be shown as ordered pairs. {(1, 5), (2, 3), (3, 2) (4, 1)}. You can also show relations in other ways, such as tables, graphs, or mapping diagrams.

  14. {(1, 5), (2, 3), (3, 2) (4, 1)}. Mapping Table Graph

  15. {(1, 5), (2, 3), (3, 2) (4, 1)}. Mapping Table Graph

  16. {(1, 5), (2, 3), (3, 2) (4, 1)}. Mapping Table Graph Points Place

  17. {(1, 5), (2, 3), (3, 2) (4, 1)}. Mapping Table Graph

  18. Table x y 2 3 4 7 6 8 Example 2: Showing Multiple Representations of Relations Express the relation {(2, 3), (4, 7), (6, 8)} as a table, as a graph, and as a mapping diagram. Write all x-values under “x” and all y-values under “y”.

  19. Example 2: Showing Multiple Representations of Relations Express the relation {(2, 3), (4, 7), (6, 8)} as a table, as a graph, and as a mapping diagram. Graph Use the x- and y-values to plot the ordered pairs.

  20. 2 3 4 7 6 8 Example 2: Showing Multiple Representations of Relations Express the relation {(2, 3), (4, 7), (6, 8)} as a table, as a graph, and as a mapping diagram. Mapping Diagram y x Write all x-values under “x” and all y-values under “y”. Draw an arrow from each x-value to its corresponding y-value.

  21. The domain of a relation is the set of first coordinates (or x-values) of the ordered pairs. The range of a relation is the set of second coordinates (or y-values) of the ordered pairs. The domain of the track meet scoring system is {1, 2, 3, 4}. The range is {1, 2, 3, 5}. Notice that domains and ranges can be written as sets.

  22. 6 –4 5 –1 2 0 1 Give the domain and range of the relation. Domain: {6, 5, 2, 1} Range: {–4, –1, 0}

  23. x y 1 1 4 4 8 1 Give the domain and range of the relation. Domain: {1, 4, 8} Range: {1, 4}

  24. 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

  25. A function is a special type of relation that pairs each domain value with exactly one range value.

  26. Give the domain and range of the relation. Tell whether the relation is a function. Explain. {(3, –2), (5, –1), (4, 0), (3, 1)} Even though 3 is in the domain twice, it is written only once when you are giving the domain. D: {3, 5, 4} R: {–2, –1, 0, 1} The relation is not a function. Each domain value does not have exactly one range value. The domain value 3 is paired with the range values –2 and 1.

  27. Give the domain and range of the relation. Tell whether the relation is a function. Explain. –4 Use the arrows to determine which domain values correspond to each range value. 2 –8 1 4 5 D: {–4, –8, 4, 5} R: {2, 1} This relation is a function. Each domain value is paired with exactly one range value.

  28. Give the domain and range of each relation. Tell whether the relation is a function and explain. a. {(8, 2), (–4, 1), (–6, 2),(1, 9)} b. D: {–6, –4, 1, 8} R: {1, 2, 9} D: {2, 3, 4} R: {–5, –4, –3}

  29. Vocabulary relation domain range function All possible values of “x” All possible values of “y” A relation where each domain value maps into EXACTLY one value in the range.

  30. Example 1 Which relation is not a function: A B NOT C Talk about height example if you don’t get slide made…

  31. Give the domain and range of the graph. Example 2 YES its a function!

  32. Give the domain and range of the graph. Example 3 NOT a Function!

  33. Vertical Line Test y If a vertical line touches the graph of a relation in more than one place the graph is NOT a function x

  34. Recognizing Functions

  35. Lesson Quiz Give the domain and range of the graph and identify if it is a function. NOT a Function!

  36. Lesson Quiz Give the domain and range of the graph and identify if it is a function. NOT a Function!

  37. Lesson Quiz

  38. Lesson Quiz

  39. Lesson Quiz

  40. Page 209: 15-25, 27-29 and 32-38b

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