Warm Up Solve. 1. x + 4 = 19 2. y – 2.3 = 7.8 3. 4z = 120 x = 15 4. = 8 x = 15 y = 10.1 z = 30 w 9 w = 72

4-4 Functions, Tables and Graphs

How does changing one variable affect another variable? Essential Question How does changing one variable affect another variable?

Definitions Function- relationship between two sets of numbers or other mathematical objects where each member of the first set is paired with only one member of the second set Input- the value substituted into the function Output- the value that results from the substitution of a given input into the function.

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.

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.

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.

A function can be represented as a rule written in words, such as “twice a 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. Rule y = 2x + 9 Output Input You can use a table to organize and display the input and output values of a function.

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

Example 2 Find the output for each input. y = 4x2 Input Rule Output x –3 4(–3)2 36 4(0)2 4 4(4)2 64

You can also use a graph to represent a function. The corresponding input and output values together form unique ordered pairs. When writing an ordered pair, write the input value first (x value) and then the output second (y value). Helpful Hint

Example 3 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

Example 4 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

Practice 2(-3)+1 -5 -(-2)+3 5 2(-5)² 50 2(0)+1 1 0+3 3 2(1)² 2 2(1)+1 -2+3 1 2(3)² 18

Practice y 4 (2, 4) 2 (1, 1) x –4 –2 2 4 (0, –2) –2 (–1, -5) –4 –6 –8 3(-1) -2 -5 (-1, -5) (1, 1) 3(0) -2 -2 (0, -2) x –4 –2 2 4 (0, –2) 3(1) -2 1 (1, 1) –2 3(2) -2 4 (2, 4) (–1, -5) –4 –6 –8 –10

Homework Workbook pg.39

1. Find the output for each input value. Closing 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

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: Input Rule Output Ordered Pair x x2 – 1 y (x, y) –2 –22 – 1 3 (-2, 3) 02 – 1 –1 (0, –1) 2 22 – 1 3 (2, 3)