Illustrative Math Alignment: Grade 8 Unit 3

Topic

Special Functions

Description

This example demonstrates a step function defined by y = floor(2x + 1) - 1. The graph features horizontal steps with points plotted at (-4, -8), (-2, -4), (0, 0), (2, 4), and (4, 8). This visual representation helps students understand how multiplying x by a coefficient greater than one affects the frequency of steps while subtracting a constant shifts them vertically.

Topic

Special Functions

Description

This example illustrates a step function defined by y = floor(-2x + 1) - 1. The graph consists of horizontal steps with points plotted at (-4, 8), (-2, 4), (0, 0), (2, -4), and (4, -8). This visual representation helps students understand how the function behaves when the input is multiplied by a negative number, a constant is added inside the floor function, and another constant is subtracted outside.

Topic

Special Functions

Description

This example demonstrates a step function defined by y = floor(0.5x + 1) - 1. The graph features horizontal steps with key points labeled, and x values (-4, -2, 0, 2, 4) corresponding to y values (-2, -1, 0, 1, 2). This visual representation helps students understand how the function behaves when the input is multiplied by a fraction, a constant is added inside the floor function, and another constant is subtracted outside.

Topic

Special Functions

Description

This example showcases a step function defined by y = floor(-2x). The table lists x values (-4, -2, 0, 2, 4) and corresponding y values (8, 4, 0, -4, -8). The graph illustrates how this function behaves, with distinct horizontal segments that demonstrate 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 and direction.

Topic

Special Functions

Description

This example illustrates a step function defined by y = floor(-0.5x + 1) - 1. The graph consists of horizontal steps with labeled points, and x values (-4, -2, 0, 2, 4) corresponding to y values (2, 1, 0, -1, -2). This visual representation helps students understand how the function behaves when the input is multiplied by a negative fraction, a constant is added inside the floor function, and another constant is subtracted outside.

Topic

Special Functions

Description

This example illustrates a step function defined by y = floor(x) - 1. The graph consists of horizontal steps with points plotted at (-4, -5), (-2, -3), (0, -1), (2, 1), and (4, 3). This visual representation helps students understand how subtracting a constant from the floor function shifts the graph vertically.

Topic

Special Functions

Description

This example demonstrates a step function defined by y = floor(2x) - 1. The graph features horizontal steps with points plotted at (-4, -9), (-2, -5), (0, -1), (2, 3), and (4, 7). This visual representation helps students understand how multiplying x by two affects the frequency of steps while subtracting one shifts them vertically.

Topic

Special Functions

Description

This example illustrates a step function defined by y = -floor(-2x) - 1. The graph displays horizontal segments at different integer values of x, 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 a negative number, the floor function is negated, and a constant is subtracted.

Topic

Special Functions

Description

This example demonstrates a step function defined by y = -floor(0.5x) - 1. The graph shows horizontal steps at different x-values, 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 fraction, the floor function is negated, and a constant is subtracted.

This is part of a collection of math examples that focus on special functions. This includes step functions and radical functions.

Topic

Special Functions

Description

This example illustrates a step function defined by y = -floor(x + 1) - 1. The graph consists of horizontal steps with points plotted at (-4, 2), (-2, 0), (0, -2), (2, -4), and (4, -6). This visual representation helps students understand how negating the floor function and adding constants both inside and outside the function affects the graph's appearance.

Topic

Special Functions

Description

This example demonstrates a step function defined by y = -floor(2x + 1) - 1. The graph features distinct horizontal steps, with x-values from -4 to 4 and corresponding y-values of 6, 2, -2, -6, and -10. This visual representation helps students understand how multiplying x by 2, adding a constant inside the floor function, and then negating and subtracting outside affects the graph's appearance.

Topic

Special Functions

Description

This example illustrates a step function defined by y = -floor(-2x + 1) - 1. The graph consists of horizontal steps, with x-values from -4 to 4 and corresponding y-values of -10, -6, -2, 2, and 6. This visual representation helps students understand how negating x inside the floor function, adding a constant, and then negating the entire function and subtracting affects the graph's appearance.

Topic

Special Functions

Description

This example demonstrates a step function defined by y = -floor(0.5x + 1) - 1. The graph features horizontal steps at various points, with x-values from -4 to 4 and corresponding y-values of 0, -1, -2, -3, and -4. This visual representation helps students understand how multiplying x by a fraction inside the floor function, adding a constant, and then negating and subtracting outside affects the graph's appearance.

Topic

Special Functions

Description

This example presents a step function defined by y = floor(0.5x). The table includes x values (-4, -2, 0, 2, 4) and corresponding y values (-2, -1, 0, 1, 2). The graph illustrates how this function behaves, with distinct horizontal segments that demonstrate the "stepping" nature of the function. This example helps students visualize how multiplying x by 0.5 inside the floor function affects the graph's appearance, particularly the width of the steps.

Topic

Special Functions

Description

This example illustrates a step function defined by y = -floor(-0.5x + 1) - 1. The graph displays horizontal steps with x-values from -4 to 4 and corresponding y-values of -4, -3, -2, -1, and 0. This visual representation helps students understand how negating and multiplying x by a fraction inside the floor function, adding a constant, and then negating the entire function and subtracting affects the graph's appearance.

Topic

Special Functions

Description

This example showcases a step function defined by y = floor(-0.5x). The table includes x-values (-4, -2, 0, 2, 4) and corresponding y-values (2, 1, 0, -1, -2). The graph illustrates how this function behaves, with distinct horizontal segments that demonstrate the "stepping" nature of the function. This example helps students visualize how multiplying x by -0.5 inside the floor function affects the graph's appearance, particularly the width and direction of the steps.

Topic

Special Functions

Description

This example demonstrates a step function defined by y = floor(x + 1). The table includes x-values (-4, -2, 0, 2, 4) and corresponding y-values (-3, -1, 1, 3, 5). The graph illustrates how this function behaves, with distinct horizontal segments that show the "stepping" nature of the function. This example helps students visualize how adding 1 to x inside the floor function affects the graph's appearance, particularly the vertical shift of the steps.

Topic

Special Functions

Description

This example showcases a step function defined by y = floor(2x + 1). The graph illustrates how this function behaves, with distinct horizontal segments at y = -7, -3, 1, 5, and 9. These steps correspond to the x-values of -4, -2, 0, 2, and 4 respectively, demonstrating how the function "steps up" as x increases.

Topic

Special Functions

Description

This example demonstrates a step function defined by y = floor(-2x + 1). The graph illustrates how this function behaves, with distinct horizontal segments at y = 9, 5, 1, -3, and -7. These steps correspond to the x-values of -4, -2, 0, 2, and 4 respectively, showing how the function "steps down" as x increases.

Topic

Special Functions

Description

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

<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 1</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 10</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 11</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 12</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

<h3>Note: The download is an image file. </h3>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 13</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 14</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 15</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 16</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 17</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 18</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 19</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 2</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 20</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 21</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 22</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 23</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 24</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 25</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 26</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 27</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 28</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 29</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 3</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 30</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 31</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 32</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 33</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 34</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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<h1>Math Example--Trig Concepts--Cosecant Functions in Tabular and Graph Form: Example 35</h1><p> This is part of a collection of math examples that focus on Trig concepts. </p>

<h3> To see the complete math example collection on this topic, <a href="https://www.media4math.com/math-examples?field_la_display_title_value=%… on this link</u></strong></a>

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