Introduction to Functions 12-1 Introduction to Functions Course 2 Warm Up Problem of the Day Lesson Presentation

Introduction to Functions Course 2 12-1 Introduction to Functions 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 w 9 w = 72

Introduction to Functions Course 2 12-1 Introduction to Functions 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

Introduction to Functions Course 2 12-1 Introduction to Functions Learn to use function tables to generate and graph ordered pairs.

Insert Lesson Title Here Course 2 12-1 Introduction to Functions Insert Lesson Title Here Vocabulary function

Introduction to Functions Course 2 12-1 Introduction to Functions 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 a single output value for each input value. A function can be represented as a rule written in words, such as “double the number and add nine to the result.”

y = 2x + 9 Introduction to Functions 12-1 Course 2 12-1 Introduction to Functions A function can also be represented by an equation with two variables. One variable represents the input, and the other represents the output. Rule y = 2x + 9 Output Input You can use a table to organize the input and output values of a function. Your table may show as many possible input and output values as you choose

Additional Example 1A: Completing a Function Table Course 2 12-1 Introduction to Functions Additional Example 1A: Completing a Function Table Find the output for each input. A. y = 8x + 5 Input Rule Output x 8x + 5 y Substitute –4 for x and simplify. –4 8(–4) + 5 –27 Substitute –2 for x and simplify. –2 8(–2) + 5 –11 Substitute 1 for x and simplify. 1 8(1) + 5 13

Additional Example 1B: Completing a Function Table Course 2 12-1 Introduction to Functions Additional Example 1B: Completing a Function Table Find the output for each input. B. y = 4x2 Input Rule Output x 4x2 y Substitute –3 for x and simplify. –3 4(–3)2 36 Substitute 0 for x and simplify. 4(0)2 Substitute 4 for x and simplify. 4 4(4)2 64

Introduction to Functions Course 2 12-1 Introduction to Functions Try This: Example 1A Find the output for each input. A. y = 5x + 3 Input Rule Output x 5x + 3 y Substitute –6 for x and simplify. –6 5(–6) + 3 –27 Substitute –3 for x and simplify. –3 5(–3) + 3 –12 Substitute 3 for x and simplify. 3 5(3) + 3 18

Introduction to Functions Course 2 12-1 Introduction to Functions Try This: Example 1B Find the output for each input. B. y = 3x2 Input Rule Output x 3x2 y Substitute –2 for x and simplify. –2 3(–2)2 12 Substitute 0 for x and simplify. 3(0)2 Substitute 5 for x and simplify. 5 3(5)2 75

Introduction to Functions Course 2 12-1 Introduction to Functions 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!

Introduction to Functions Course 2 12-1 Introduction to Functions When writing an ordered pair, write the input value first and then the output value. Helpful Hint

Additional Example 2A: Graphing Functions Using Ordered pairs Course 2 12-1 Introduction to Functions Additional Example 2A: Graphing Functions Using Ordered pairs Make a function table and graph the resulting ordered pairs. y A. 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

Additional Example 2B: Graphing Functions with Ordered Pairs Course 2 12-1 Introduction to Functions Additional Example 2B: Graphing Functions with Ordered Pairs Make a function table and graph the resulting ordered pairs. y B. y = 5x2 (–2, 20) (2, 20) 20 Ordered Pair Input Rule Output 16 x 5x2 y (x, y) 12 –2 5(–2)2 20 (–2, 20) 8 –1 5(–1)2 5 (–1, 5) (–1, 5) (1, 5) 5(0)2 4 (0, 0) (0,0) 1 5(1)2 5 (1, 5) –8 –4 O 4 8 x 2 5(2)2 20 (2, 20)

Introduction to Functions Course 2 12-1 Introduction to Functions Try This: Example 2A Make a function table and graph the resulting ordered pairs. y A. 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

Introduction to Functions Course 2 12-1 Introduction to Functions Try This: Example 2B Make a function table and graph the resulting ordered pairs. y B. 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

Introduction to Functions Insert Lesson Title Here Course 2 12-1 Introduction to Functions Insert Lesson Title Here Lesson Quiz: Part 1 Find the output for each input value. Input Rule Output x 4x – 1 y –2 –9 –1 4 15

Introduction to Functions Insert Lesson Title Here Course 2 12-1 Introduction to Functions Insert Lesson Title Here Lesson Quiz: Part 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: x y –2 3 –1 2