Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 3

Functions and Volume

Lesson 4: Tables, Equations, and Graphs of Functions

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 17 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 17 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 17

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 18 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 18 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 18

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 19 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 19 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 19

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 2 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 2 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 2

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 20 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 20 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 20

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 21 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 21 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 21

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 22 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 22 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 22

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 23 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 23 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 23

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 24 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 24 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 24

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 25 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 25 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 25

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 26 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 26 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 26

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 27 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 27 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 27

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 28 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 28 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 28

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 29 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 29 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 29

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 3 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 3 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 3

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 30 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 30 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 30

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 31 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 31 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 31

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 32 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 32 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 32

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 33 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 33 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 33

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 34 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 34 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 34

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 35 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 35 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 35

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 36 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 36 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 36

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 37 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 37 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 37

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 38 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 38 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 38

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 39 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 39 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 39

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 4 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 4 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 4

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 40 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 40 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 40

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 5 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 5 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 5

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 6 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 6 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 6

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 7 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 7 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 7

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 8 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 8 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 8

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 9 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 9 Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 9

Topic

Radical Functions

 Radical Functions and Equations
Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 1 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 1 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 1

Topic

Special Functions

 Special Functions
Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 10 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 10 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 10

Topic

Special Functions

Description

This example presents a step function defined by y = floor(-0.5x + 1). The graph shows horizontal segments stepping down as x increases. The table contains x values (-4, -2, 0, 2, 4) and their corresponding y values (3, 2, 1, 0, -1), illustrating how the function behaves at these specific points.

 Special Functions
Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 11 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 11 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 11

Topic

Special Functions

Description

This example illustrates a step function defined by y = floor(2x) + 1. The table shows x values (-4, -2, 0, 2, 4) and their corresponding y values (-7, -3, 1, 5, 9). The graph displays horizontal steps increasing as x increases, demonstrating how the function behaves across different intervals.

 Special Functions
Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 12 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 12 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 12

Topic

Special Functions

Description

This example demonstrates a step function defined by y = floor(-2x) + 1. The table shows x values (-4, -2, 0, 2, 4) and their corresponding y values (9, 5, 1, -3, -7). The graph displays horizontal line segments stepping down as x increases, illustrating how the function behaves across different intervals.

 Special Functions
Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 13 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 13 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 13

Topic

Special Functions

Description

This example showcases a step function defined by y = floor(-2x) + 1. The graph features red horizontal segments and black points at key coordinates, with x values of -4, -2, 0, 2, and 4, and corresponding y values of 9, 5, 1, -3, and -7. This visual representation helps students understand how the function behaves across different intervals.

 Special Functions
Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 14 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 14 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 14

Topic

Special Functions

Description

This example illustrates a step function defined by y = floor(0.5x) + 1. The graph features red horizontal segments and black points at key coordinates, with x values of -4, -2, 0, 2, and 4, and corresponding y values of -1, 0, 1, 2, and 3. This visual representation helps students understand how the function behaves when the coefficient of x is a fraction.

 Special Functions
Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 15 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 15 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 15

Topic

Special Functions

Description

This example demonstrates a step function defined by y = floor(-0.5x) + 1. The graph features red horizontal segments and black points at key coordinates, with x values of -4, -2, 0, 2, and 4, and corresponding y values of 3, 2, 1, 0, and -1. This visual representation helps students understand how the function behaves when the coefficient of x is a negative fraction.

 Special Functions
Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 16 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 16 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 16

Topic

Special Functions

Description

This example illustrates a step function defined by y = floor(x + 1) + 1. The graph features red horizontal segments and black points at key coordinates, with x values of -4, -2, 0, 2, and 4, and corresponding y values of -2, 0, 2, 4, and 6. This visual representation helps students understand how the function behaves across different intervals.

 Special Functions
Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 17 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 17 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 17

Topic

Special Functions

Description

This example demonstrates a step function defined by y = floor(2x + 1) + 1. The graph is plotted with points (-4, -6), (-2, -2), (0, 2), (2, 6), and (4, 10), showing horizontal steps that increase as x increases. This visual representation helps students understand how the function behaves when there's a coefficient greater than 1 inside the floor function.

 Special Functions
Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 18 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 18 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 18

Topic

Special Functions

Description

This example showcases a step function defined by y = floor(-2x + 1) + 1. The graph consists of horizontal steps decreasing sharply as x increases, with points plotted at (-4, 10), (-2, 6), (0, 2), (2, -2), and (4, -6). This visual representation helps students understand how the function behaves when there's a negative coefficient inside the floor function.

 Special Functions
Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 19 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 19 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 19

Topic

Special Functions

Description

This example illustrates a step function defined by y = floor(0.5x + 1) + 1. The graph consists of horizontal steps increasing gradually as x increases, with points plotted at (-4, 0), (-2, 1), (0, 2), (2, 3), and (4, 4). This visual representation helps students understand how the function behaves when there's a fractional coefficient inside the floor function.

 Special Functions
Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 2 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 2 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 2

Topic

Special Functions

Description

This example demonstrates a step function defined by y = floor(2x). The table presents x values (-4, -2, 0, 2, 4) and corresponding y values (-8, -4, 0, 4, 8). The graph shows how this function behaves, with distinct horizontal segments that illustrate the "stepping" nature of the function. This example helps students visualize how multiplying x by 2 inside the floor function affects the graph's appearance.

 Special Functions
Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 20 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 20 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 20

Topic

Special Functions

Description

This example demonstrates a step function defined by y = floor(-0.5x + 1) + 1. The graph consists of horizontal steps decreasing from left to right, with points plotted at (-4, 4), (-2, 3), (0, 2), (2, 1), and (4, 0). This visual representation helps students understand how the function behaves when there's a negative fractional coefficient inside the floor function.

 Special Functions
Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 21 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 21 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 21

Topic

Special Functions

Description

This example illustrates a step function defined by y = floor(x) - 1. The graph features horizontal steps at each integer value of x, with points plotted at (-4, -5), (-2, -3), (0, -1), (2, 1), and (4, 3). This visual representation helps students understand how the function behaves when a constant is subtracted from the floor function.

 Special Functions
Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 22 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 22 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 22

Topic

Special Functions

Description

This example demonstrates a step function defined by y = floor(2x) - 1. The graph features horizontal steps that increase as x increases, with points plotted at (-4, -9), (-2, -5), (0, -1), (2, 3), and (4, 7). This visual representation helps students understand how the function behaves when the input is multiplied by 2 and a constant is subtracted from the floor function.

 Special Functions
Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 23 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 23 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 23

Topic

Special Functions

Description

This example illustrates a step function defined by y = floor(-2x) - 1. The graph features horizontal steps that decrease as x increases, with points plotted at (-4, 7), (-2, 3), (0, -1), (2, -5), and (4, -9). This visual representation helps students understand how the function behaves when the input is multiplied by a negative number and a constant is subtracted from the floor function.

 Special Functions
Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 24 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 24 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 24

Topic

Special Functions

Description

This example demonstrates a step function defined by y = floor(0.5x) - 1. The graph features horizontal steps that increase slowly as x increases, with points plotted at (-4, -3), (-2, -2), (0, -1), (2, 0), and (4, 1). This visual representation helps students understand how the function behaves when the input is multiplied by a fraction and a constant is subtracted from the floor function.

 Special Functions
Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 25 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 25 Math Example--Special Functions--Step Functions in Tabular and Graph Form: Example 25

Topic

Special Functions

Description

This example illustrates a step function defined by y = floor(-0.5x) - 1. The graph is a series of horizontal steps, with points plotted at (-4, 1), (-2, 0), (0, -1), (2, -2), and (4, -3). This visual representation helps students understand how the function behaves when the input is multiplied by a negative fraction and a constant is subtracted from the floor function.

 Special Functions