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# Chapter 4.8: Determine if the Relation is a Function

Chapter 4.8: Determine if the Relation is a Function. Lesson 4.8: Function &amp; Relations. Definition. Relation: Any set of ordered pairs. Function: A rule that establishes a relationship between 2 quantities, the input and the output. For every x there is exactly one y. Domain: x values.

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## Chapter 4.8: Determine if the Relation is a Function

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1. Chapter 4.8: Determine if the Relation is a Function

2. Lesson 4.8: Function & Relations Definition Relation: Any set of ordered pairs Function: A rule that establishes a relationship between 2 quantities, the input and the output. For every x there is exactly one y Domain: x values Input: x values Range: y values Output: y values Set Notation {1,2,3} Only write the number once, even if it repeats

3. Lesson 4.8: Determining if the relation is a function To determine if a given relation is a function, we use the vertical line test. If the vertical line intersects the relation at one point as it moves across the graph, then that graph is a function. If the vertical line intersects the relation at more than one point as it moves across the graph, then that graph is NOT a function.

4. y x Lesson 4.8: Determining if the relation is a function- Vertical Line Test Run a vertical line across the page from left to right Since the line only touched once, there is only one x value for every y, it is a function.

5. y x Lesson 4.8: Determining if the relation is a function- Vertical Line Test Run a vertical line across the page from left to right Since the line touched more than once, there is more than one x value for every y, it is a function.

6. Lesson 4.8: Determining if the relation is a function given a table of values Step 1: Graph each point Input Output xy {1,2,3,4} Domain: 1 3 4 1 2 3 4 1 1 2 3 {1,3,4} Range: 3 3 4 4 Step 2: Conduct vertical line test.

7. y x Lesson 4.8: Determining if the relation is a function given a table of values Step 1: Graph each point Input Output Step 2: Vertical Line Test 1 2 3 4 1 3 4 Since the line only touched once, there is only one x value for every y, it is a function.

8. Lesson 4.8: Determining if the relation is a function given a table of values y x Step 1: Graph each point Input Output Step 2: Vertical Line Test 1 3 4 4 Since the line touched more than once, there is more than one x value for every y, it is a function.

9. Lesson 4.8: Determining if the relation is a function given a table of values Input Output Input Output 1 3 4 1 2 3 4 1 3 4 4

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