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Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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**Warm Up Solve. 1. x + 4 = 19 2. y – 2.3 = 7.8 3. 4z = 120 x = 15**

= 8 x = 15 y = 10.1 z = 30 w 9 w = 72

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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. 1 aa + ab = ac – a = 2, b = 3, c =1

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**Sunshine State Standards**

Prep for MA.7.A.1.4 Graph proportional relationships… Review of MA.6.A.3.6

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Vocabulary function input output

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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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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. Function Rule y = 2x + 9 Output variable Input variable You can use a table to organize and display the input and output values of a function.

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**Additional Example 1A: Completing a Function Table**

Find the output for each input. y = 8x + 5 Input Rule Output x 8x + 5 y Substitute –4 for x. Then simplify. –4 8(–4) + 5 –27 Substitute –2 for x. Then simplify. –2 8(–2) + 5 –11 Substitute 1 for x. Then simplify. 1 8(1) + 5 13

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**Additional Example 1B: Completing a Function Table**

Find the output for each input. y = 4x2 Input Rule Output x 4x2 y Substitute –5 for x. Then simplify. –5 4(–5)2 100 Substitute 0 for x. Then simplify. 4(0)2 Substitute 5 for x. Then simplify. 5 4(5)2 100

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

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Check It Out: Example 1B Find the output for each input. y = 3x2 Input Rule Output x 3x2 y Substitute –2 for x. Then simplify. –2 3(–2)2 12 Substitute 0 for x. Then simplify. 3(0)2 Substitute 5 for x. Then simplify. 5 3(5)2 75

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**You can also use a graph to represent a **

function. The corresponding input and output values together form unique ordered pairs. An ordered pair is a pair of numbers that represents a point on a graph. Remember!

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**When writing an ordered pair, write the input value first and then the output value.**

Helpful Hint

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**Additional Example 2A: Graphing Functions Using Ordered Pairs**

Make a function table for x = –2, –1, 0, 1, and 2, and graph the resulting ordered pairs. y y = 3x – 4 4 Ordered Pair 2 (2, 2) Input Rule Output x 3x – 4 y (x, y) x –4 –2 2 4 (1, –1) –2 3(–2) – 4 –10 (–2, –10) –2 (0, –4) –1 3(–1) – 4 –7 (–1, –7) –4 3(0) – 4 –4 (0, –4) –6 (–1, –7) 1 3(1) – 4 –1 (1, –1) –8 2 3(2) – 4 2 (2, 2) (–2, –10) –10

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**Additional Example 2B: Graphing Functions Using Ordered Pairs**

Make a function table for x = –2, –1, 0, 1, and 2, and graph the resulting ordered pairs. y = x2 + 1 Ordered Pair Input Rule Output y x x2 + 1 y (x, y) 6 (–2, 5) (2, 5) –2 (–2)2 + 1 5 (–2, 5) 4 –1 (–1)2 + 1 2 (–1, 2) (–1, 2) (1, 2) 2 (0)2 + 1 1 (0, 1) (0,1) 1 (1)2 + 1 2 (1, 2) –4 –2 O 2 4 x 2 (2)2 + 1 5 (2, 5)

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

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Check It Out: Example 2B Make a function table for x = –2, –1, 0, 1, and 2, and graph the resulting ordered pairs. y y = 6x2 (–2, 24) (2, 24) Ordered Pair Input Rule Output 20 x 6x2 y (x, y) 16 –2 6(–2)2 24 (–2, 24) 12 –1 6(–1)2 6 (–1, 6) 8 6(0)2 (0, 0) (–1, 6) (1, 6) 1 6(1)2 6 (1, 6) 4 (0,0) 2 6(2)2 24 (2, 24) –8 –4 O 4 8 x

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Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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**1. Find the output for each input value.**

Lesson Quiz: Part I 1. Find the output for each input value. Input Rule Output x 4x – 1 y –2 4(–2) – 1 –9 4(0) – 1 –1 4 4(4) – 1 15

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Lesson Quiz: Part II 2. Make a function table with three input values for y = x2 – 1, and graph the resulting ordered pairs. x y –2 2 –4 4 (–2, 3) (2, 3) (0, –1) Possible answer: Output Ordered Pair Rule Input x x2 – 1 y (x, y) –2 –22 – 1 3 (–2, 3) 02 – 1 –1 (0, –1) 2 22 – 1 3 (2, 3)

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**Lesson Quiz for Student Response Systems**

1. Identify the output for each input. A B.

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**Lesson Quiz for Student Response Systems**

2. Identify a function table for y = x2 – 3, and graph the resulting ordered pairs. A B.

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Warm Up Solve. 1. x + 4 = 19 2. y – 2.3 = 7.8 3. 4z = 120 4. = 8 x = 15 y = 10.1 z = 30 Course 2 12-1 Introduction to Functions w9w9 w = 72 Learning Target:

Warm Up Solve. 1. x + 4 = 19 2. y – 2.3 = 7.8 3. 4z = 120 4. = 8 x = 15 y = 10.1 z = 30 Course 2 12-1 Introduction to Functions w9w9 w = 72 Learning Target:

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