4-4 Functions, Tables, and Graphs Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

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 – Course Functions, Tables, and Graphs

Learn to use function tables to generate and graph ordered pairs. Course Functions, Tables, and Graphs

Vocabulary function input output Insert Lesson Title Here Course 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. Course Functions, Tables, and Graphs

Rule Output Input You can use a table to organize and display the input and output values of a function. Course Functions, Tables, and Graphs 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.

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 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 Functions, Tables, and Graphs

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 y = 4x 2 Rule Output x 4x24x2 y – (–3) 2 4(0) 2 4(4) Course Functions, Tables, and Graphs

Check It Out: 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 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 Functions, Tables, and Graphs

Check It Out: 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 y = 3x 2 Rule Output x 3x23x2 y – (–2) 2 3(0) 2 3(5) Course 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. Course Functions, Tables, and Graphs

When writing an ordered pair, write the input value first and then the output value. Helpful Hint Course 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 with 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) Course Functions, Tables, and Graphs

Additional Example 2B: Graphing Functions with Ordered Pairs y = 5x 2 Make a function table for x = -2, -1, 0, 1, and 2, 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 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 Course 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 Course Functions, Tables, and Graphs

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

Lesson Quiz: Part II 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: x y –2 2 2 –4 4 4 (–2, 3) (2, 3) (0, –1) Course Functions, Tables, and Graphs InputRuleOutputOrdered Pair x 2 – 1 y x – – – 1 –2 2 – – 1 (x, y) (-2, 3) (0, –1) (2, 3)