1. 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: I can use function tables to generate and graph ordered pairs.

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

3. 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.” Course 2 12-1 Introduction to Functions

4. A function can also be represented by an equation with two variables. One variable represents the input, and the other represents the output. Rule 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 Course 2 12-1 Introduction to Functions

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

6. Additional Example 1B: Completing a Function Table Substitute –3 for x and simplify. Substitute 0 for x and simplify. Substitute 4 for x and simplify. Find the output for each input. Input B. y = 4x 2 Rule Output x 4x24x2 y –3 0 4 4(–3) 2 4(0) 2 4(4) 2 36 0 64 Course 2 12-1 Introduction to Functions

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

8. Try This: Example 1B Substitute –2 for x and simplify. Substitute 0 for x and simplify. Substitute 5 for x and simplify. Find the output for each input. Input B. y = 3x 2 Rule Output x 3x23x2 y –2 0 5 3(–2) 2 3(0) 2 3(5) 2 12 0 75 Course 2 12-1 Introduction to Functions

9. 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. Course 2 12-1 Introduction to Functions

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

11. Make a function table 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 0 1 2 3(–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 A. y = 3x – 4 (–2, –10) (–1, –7) (0, –4) (1, –1) (2, 2) Course 2 12-1 Introduction to Functions

12. Additional Example 2B: Graphing Functions with Ordered Pairs B. y = 5x 2 Make a function table and graph the resulting ordered pairs. RuleInput Output Ordered Pair 5(–2) 2 x 5x25x2 y (–2, 20)–2 –1 0 1 2 5(–1) 2 5(0) 2 5(1) 2 5(2) 2 20 5 0 5 (–1, 5) (0, 0) (1, 5) (2, 20) (x, y) x 16 20 48–8 12 8 O 4 –4 (0,0) (–1, 5)(1, 5) (2, 20) y (–2, 20) Course 2 12-1 Introduction to Functions

13. Make a function table 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 0 1 2 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 A. y = 2x – 3 (–2, –7) (–1, –5) (0, –3) (1, –1) (2, 1) Try This: Example 2A Course 2 12-1 Introduction to Functions

14. B. y = 6x 2 Make a function table and graph the resulting ordered pairs. RuleInput Output Ordered Pair 6(–2) 2 x 6x26x2 y (–2, 24)–2 –1 0 1 2 6(–1) 2 6(0) 2 6(1) 2 6(2) 2 24 6 0 6 (–1, 6) (0, 0) (1, 6) (2, 24) (x, y) x 16 20 48–8 12 8 O 4 –4 (0,0) (–1, 6)(1, 6) (2, 24) y (–2, 24) Try This: Example 2B Course 2 12-1 Introduction to Functions

15. Assignment Page 606 #6-10 Make sure to draw graphs with a ruler for Number 9 & 10. Course 2 12-1 Introduction to Functions Learning Target: I can use function tables to generate and graph ordered pairs.

16. Lesson Quiz: Part 1 Find the output for each input value. Insert Lesson Title Here Input RuleOutput 4x – 1yx –2 0 4 –9 –1 15 Course 2 12-1 Introduction to Functions

17. Lesson Quiz: Part 2 Make a function table with three input values for y = x 2 – 1, and graph the resulting ordered pairs. Insert Lesson Title Here Possible answer: xy –23 0–1–1 23 x y 2 2 –4 4 4 (–2, 3) (2, 3) (0, –1) Course 2 12-1 Introduction to Functions