Illustrative Math Alignment: Grade 8 Unit 3

Topic

Radical Functions

Topic

Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

Topic

Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Radical Functions

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Special Functions

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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, -4), (-2, -2), (0, 0), (2, 2), and (4, 4). This visual representation helps students understand how the function behaves when a constant is added inside the floor function and another constant is subtracted outside.