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Holt Algebra Relations and Functions 1-6 Relations and Functions Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

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Holt Algebra Relations and Functions Do Now Use the graph for Problems 1–2. 1. List the x-coordinates of the points. 2. List the y-coordinates of the points.

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Holt Algebra Relations and Functions TSW identify the domain and range of relations and functions. TSW determine whether a relation is a function. Objectives

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Holt Algebra Relations and Functions relation domain range function Vocabulary

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Holt Algebra Relations and Functions A relation is a pairing of input values with output values. It can be shown as a set of ordered pairs (x,y), where x is an input and y is an output. The set of input values for a relation is called the domain, and the set of output values is called the range.

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Holt Algebra Relations and Functions A B C 2 DomainRange Mapping Diagram Set of Ordered Pairs {(2, A), (2, B), (2, C)} (x, y) (input, output) (domain, range)

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Holt Algebra Relations and Functions Example 1: Identifying Domain and Range Give the domain and range for this relation: {(100,5), (120,5), (140,6), (160,6), (180,12)}. Domain: Range: List the set of ordered pairs:

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Holt Algebra Relations and Functions Example 2 Give the domain and range for the relation shown in the graph. List the set of ordered pairs:

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Holt Algebra Relations and Functions Suppose you are told that a person entered a word into a text message using the numbers 6, 2, 8, and 4 on a cell phone. It would be difficult to determine the word without seeing it because each number can be used to enter three different letters.

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Holt Algebra Relations and Functions Number {Number, Letter} {(8, T), (8, U), (8, V)} {(6, M), (6, N), (6, O)} {(2, A), (2, B), (2, C)} {(4, G), (4, H), (4, I)} The numbers 6, 2, 8, and 4 each appear as the first coordinate of three different ordered pairs.

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Holt Algebra Relations and Functions However, if you are told to enter the word MATH into a text message, you can easily determine that you use the numbers 6, 2, 8, and 4, because each letter appears on only one numbered key. {(M, 6), (A, 2), (T, 8), (H,4)} The first coordinate is different in each ordered pair. A relation in which the first coordinate is never repeated is called a function. In a function, there is only one output for each input, so each element of the domain is mapped to exactly one element in the range.

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Holt Algebra Relations and Functions Although a single input in a function cannot be mapped to more than one output, two or more different inputs can be mapped to the same output.

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Holt Algebra Relations and Functions Not a function: The relationship from number to letter is not a function because the domain value 2 is mapped to the range values A, B, and C. Function: The relationship from letter to number is a function because each letter in the domain is mapped to only one number in the range.

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Holt Algebra Relations and Functions Example 3: Determining Whether a Relation is a Function Determine whether each relation is a function. A. from the items in a store to their prices on a certain date B. from types of fruits to their colors

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Holt Algebra Relations and Functions Example 4 A. Determine whether each relation is a function. B. from the number of items in a grocery cart to the total cost of the items in the cart

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Holt Algebra Relations and Functions Every point on a vertical line has the same x-coordinate, so a vertical line cannot represent a function. If a vertical line passes through more than one point on the graph of a relation, the relation must have more than one point with the same x- coordinate. Therefore the relation is not a function.

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Holt Algebra Relations and Functions

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Holt Algebra Relations and Functions Use the vertical-line test to determine whether the relation is a function. If not, identify two points a vertical line would pass through. Example 5: Using the Vertical-Line Test

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Holt Algebra Relations and Functions Use the vertical-line test to determine whether the relation is a function. If not, identify two points a vertical line would pass through. Example 6: Using the Vertical-Line Test

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Holt Algebra Relations and Functions Example 7 Use the vertical-line test to determine whether the relation is a function. If not, identify two points a vertical line would pass through.

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Holt Algebra Relations and Functions This is not a function. A vertical line at x = 1 would pass through (1, 2) and (1, –2). Example 8 Use the vertical-line test to determine whether the relation is a function. If not, identify two points a vertical line would pass through.

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Holt Algebra Relations and Functions Lesson Quiz: Part I 1. Give the domain and range for this relation: {(10, 5), (20, 5), (30, 5), (60, 100), (90, 100)}. Determine whether each relation is a function. 2. from each person in class to the number of pets he or she has 3. from city to zip code

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Holt Algebra Relations and Functions Lesson Quiz: Part II Use the vertical-line test to determine whether the relation is a function. If not, identify two points a vertical line would pass through. 4.

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Holt Algebra Relations and Functions Lesson Quiz: Part I 1. Give the domain and range for this relation: {(10, 5), (20, 5), (30, 5), (60, 100), (90, 100)}. Determine whether each relation is a function. 2. from each person in class to the number of pets he or she has 3. from city to zip code function not a function D: {10, 20, 30, 60, 90)} R: {5, 100}

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Holt Algebra Relations and Functions Lesson Quiz: Part II Use the vertical-line test to determine whether the relation is a function. If not, identify two points a vertical line would pass through. 4. not a function; possible answer: (3, 2) and (3, –2)

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