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5-2 Functions, Tables, and Graphs Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

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5-2 Functions, Tables, and Graphs Warm Up Solve. 1. x + 4 = y – 2.3 = z = = 8 x = 15 y = 10.1 z = 30 w9w9 w = 72

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5-2 Functions, Tables, and Graphs Problem of the Day Substitute the numbers 1, 2, and 3 for the letters a, b, and c in such a way that the number sentence is correct. a = 2, b = 3, c =1 1aa1aaa + 1ab1ab = 1ac1ac 1ab1ab –

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5-2 Functions, Tables, and Graphs Prep for MA.7.A.1.4 Graph proportional relationships… Review of MA.6.A.3.6 Sunshine State Standards

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5-2 Functions, Tables, and Graphs Vocabulary function input output

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5-2 Functions, Tables, and Graphs Rube Goldberg, a famous cartoonist, invented machines that perform ordinary tasks in extraordinary ways. Each machine operates according to a rule, or a set of steps, to produce a particular output. In mathematics, a function operates according to a rule to produce exactly one output value for each input value. The input is the value substituted into the function. The output is the value that results from the substitution of a given input into the function.

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5-2 Functions, Tables, and Graphs Function Rule Output variable Input variable You can use a table to organize and display the input and output values of a function. A function can be represented as a rule written in words, such as double the number and add nine to the result, or by an equation with two variables. One variable represents the input, and the other represents the output.

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5-2 Functions, Tables, and Graphs Additional Example 1A: Completing a Function Table Substitute –4 for x. Then simplify. Substitute –2 for x. Then simplify. Substitute 1 for x. Then simplify. Find the output for each input. Input y = 8x + 5 Rule Output x 8x + 5 y –4 –2 1 8(–4) + 5 8(–2) + 5 8(1) + 5 –27 –11 13

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5-2 Functions, Tables, and Graphs Additional Example 1B: Completing a Function Table Substitute –5 for x. Then simplify. Substitute 0 for x. Then simplify. Substitute 5 for x. Then simplify. Find the output for each input. Input y = 4x 2 Rule Output x 4x24x2 y – (–5) 2 4(0) 2 4(5)

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5-2 Functions, Tables, and Graphs Check It Out: Example 1A Substitute –6 for x. Then simplify. Substitute –3 for x. Then simplify. Substitute 3 for x. Then simplify. Find the output for each input. Input y = 5x + 3 Rule Output x 5x + 3 y –6 –3 3 5(–6) + 3 5(–3) + 3 5(3) + 3 –27 –12 18

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5-2 Functions, Tables, and Graphs Check It Out: Example 1B Substitute –2 for x. Then simplify. Substitute 0 for x. Then simplify. Substitute 5 for x. Then simplify. Find the output for each input. Input y = 3x 2 Rule Output x 3x23x2 y – (–2) 2 3(0) 2 3(5)

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5-2 Functions, Tables, and Graphs An ordered pair is a pair of numbers that represents a point on a graph. Remember! You can also use a graph to represent a function. The corresponding input and output values together form unique ordered pairs.

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5-2 Functions, Tables, and Graphs When writing an ordered pair, write the input value first and then the output value. Helpful Hint

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5-2 Functions, Tables, and Graphs Make a function table for x = –2, –1, 0, 1, and 2, and graph the resulting ordered pairs. Additional Example 2A: Graphing Functions Using Ordered Pairs x y RuleInput Output Ordered Pair 3(–2) – 4 x 3x – 4 y (–2, –10) 2 4 –2 – (–1) – 4 3(0) – 4 3(1) – 4 3(2) – 4 –10 –7 –4 –1 2 (–1, –7) (0, –4) (1, –1) (2, 2) (x, y) 2 4 –2 –4 –10 –6 –8 –4 y = 3x – 4 (–2, –10) (–1, –7) (0, –4) (1, –1) (2, 2)

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5-2 Functions, Tables, and Graphs Additional Example 2B: Graphing Functions Using Ordered Pairs y = x Make a function table for x = –2, –1, 0, 1, and 2, and graph the resulting ordered pairs. RuleInput Output Ordered Pair (–2) xx 2 + 1y (–2, 5)–2 – (–1) (0) (1) (2) (–1, 2) (0, 1) (1, 2) (2, 5) (x, y) x 24–4 6 4 O 2 –2 (0,1) (–1, 2)(1, 2) (2, 5) y (–2, 5)

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5-2 Functions, Tables, and Graphs Make a function table for x = –2, –1, 0, 1, and 2, and graph the resulting ordered pairs. x y RuleInput Output Ordered Pair 2(–2) – 3 x 2x – 3 y (–2, –7) 2 4 –2 – (–1) – 3 2(0) – 3 2(1) – 3 2(2) – 3 –7 –5 –3 –1 1 (–1, –5) (0, –3) (1, –1) (2, 1) (x, y) 2 4 –2 –4 –10 –6 –8 –4 y = 2x – 3 (–2, –7) (–1, –5) (0, –3) (1, –1) (2, 1) Check It Out: Example 2A

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5-2 Functions, Tables, and Graphs y = 6x 2 Make a function table for x = –2, –1, 0, 1, and 2, and graph the resulting ordered pairs. Rule Input Output Ordered Pair 6(–2) 2 x 6x26x2 y (–2, 24)–2 – (–1) 2 6(0) 2 6(1) 2 6(2) (–1, 6) (0, 0) (1, 6) (2, 24) (x, y) x – O 4 –4 (0,0) (–1, 6)(1, 6) (2, 24) y (–2, 24) Check It Out: Example 2B

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5-2 Functions, Tables, and Graphs Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

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5-2 Functions, Tables, and Graphs Lesson Quiz: Part I 1. Find the output for each input value. Input RuleOutput 4x – 1yx –2 0 4 –9 –1 15 4(–2) – 1 4(0) – 1 4(4) – 1

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5-2 Functions, Tables, and Graphs Lesson Quiz: Part II 2. Make a function table with three input values for y = x 2 – 1, and graph the resulting ordered pairs. Possible answer: x y –2 2 2 –4 4 4 (–2, 3) (2, 3) (0, –1) OutputOrdered Pair RuleInput x 2 – 1 y x – – – 1 –2 2 – – 1 (x, y) (–2, 3) (0, –1) (2, 3)

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5-2 Functions, Tables, and Graphs 1. Identify the output for each input. A. B. Lesson Quiz for Student Response Systems

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5-2 Functions, Tables, and Graphs 2. Identify a function table for y = x 2 – 3, and graph the resulting ordered pairs. A. B. Lesson Quiz for Student Response Systems

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