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

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Presentation on theme: "#1#1 Find the value of y for each of the following values of x: #2#2 #3#3 #4#4 Find the value of x for each of the following values of y: #5#5."— Presentation transcript:

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

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

3 #2#2 #1#1

4 #2#2 #3#3 #1#1

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

6 #4#4 #5#5

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

8 xy Table

9 Ordered Pair xy Table

10 Ordered Pair Y-axis X-axis Graph

11 relation domain range function Vocabulary

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 a relation.

13 The scoring systems of a track meets is as follows: 1 st place: 5 points 2 nd place: 3 points 3 rd place: 2 points 4 th place: 1 point Relationships can also be represented by a set of ordered pairs called a relation. For example : 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)}. Table Graph Mapping

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

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

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

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

19 Use the x- and y-values to plot the ordered pairs. Graph 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.

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

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

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

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

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)} R: {–2, –1, 0, 1} D: {3, 5, 4} Even though 3 is in the domain twice, it is written only once when you are giving the domain. 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 –4 – D: {–4, –8, 4, 5} R: {2, 1} Use the arrows to determine which domain values correspond to each range value. This relation is a function. Each domain value is paired with exactly one range value. Give the domain and range of the relation. Tell whether the relation is a function. Explain.

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 relation domain range function Vocabulary 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 AA Which relation is not a function: BB CC NOT Talk about height example if you dont get slide made…

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

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

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

34 Recognizing Functions

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

37 Lesson Quiz

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

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