Warm Up Solve. 1. x + 4 = y – 2.3 = z = = 8 x = 15 y = 10.1 z = 30 Course Introduction to Functions w9w9 w = 72 Learning Target: I can use function tables to generate and graph ordered pairs.

Vocabulary function Insert Lesson Title Here Course 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.” Course 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 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 Introduction to Functions

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 Introduction to Functions

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) 2 4(0) 2 4(4) Course Introduction to Functions

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 Introduction to Functions

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) 2 3(0) 2 3(5) Course Introduction to Functions

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 Introduction to Functions

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

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) – 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 Introduction to Functions

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) 2 5(0) 2 5(1) 2 5(2) (–1, 5) (0, 0) (1, 5) (2, 20) (x, y) x – O 4 –4 (0,0) (–1, 5)(1, 5) (2, 20) y (–2, 20) Course Introduction to Functions

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) – 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 Introduction to Functions

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) 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) Try This: Example 2B Course Introduction to Functions

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

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 Introduction to Functions

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 Introduction to Functions