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**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

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**Find the value of y for each of the following values of x:**

#1

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**Find the value of y for each of the following values of x:**

#1 #2

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**Find the value of y for each of the following values of x:**

#1 #2 #3

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**Find the value of x for each of the following values of y:**

#4 #5

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**Find the value of x for each of the following values of y:**

#4 #5

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**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

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Table x y

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Table Ordered Pair x y

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Graph Y-axis Ordered Pair X-axis

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Vocabulary relation domain range function

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**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.

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**Relationships can also be represented by a set of ordered pairs called a relation.**

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.

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

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

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

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

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**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. x y Table Write all x-values under “x” and all y-values under “y”. 2 4 6 3 7 8

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**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.

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**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 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. 2 6 4 3 8 7

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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.

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**Give the domain and range of the relation.**

1 2 6 5 –4 –1 Domain: {6, 5, 2, 1} Range: {–4, –1, 0}

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

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**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

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

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**Give the domain and range of the relation**

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.

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**Give the domain and range of the relation**

Give the domain and range of the relation. Tell whether the relation is a function. Explain. –4 2 Use the arrows to determine which domain values correspond to each range value. –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.

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**Give the domain and range of each relation**

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}

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**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.

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**Which relation is not a function:**

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

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**Give the domain and range of the graph.**

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

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**Give the domain and range of the graph.**

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

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**y x Vertical Line Test If a vertical line touches**

the graph of a relation in more than one place the graph is NOT a function x

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**Recognizing Functions**

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

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

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Lesson Quiz

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Lesson Quiz

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Lesson Quiz

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

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Relations and Functions

Relations and Functions

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