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.
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 26 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 26TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = 1 / (-x - 1) - 1. The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The graph shows points plotted at (-2, 0), (-1.5, 1), (0, -2), (1.5, -1.4), and (2, -1.333), illustrating how negating both terms inside the parentheses and subtracting a constant from the entire fraction affects the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 27 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 27TopicRational Functions DescriptionThis math example illustrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (-x - 1) + 1. The image presents both the table of x-y coordinates and the resulting graph. The graph shows points plotted at (-2, 0), (-1.5, -1), (0, 2), (1.5, 1.4), and (2, 1.333), demonstrating how negating both the numerator and the terms inside the parentheses, while adding a constant to the entire fraction, affects the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 28 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 28TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (-x - 1) - 1. The image showcases both the table of x-y coordinates and the resulting graph. The graph shows points plotted at (-2, -2), (-1.5, -3), (0, 0), (1.5, -0.6), and (2, -0.667), illustrating how negating both the numerator and the terms inside the parentheses, while subtracting a constant from the entire fraction, affects the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 3 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 3TopicRational Functions DescriptionThis math example illustrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (-x). The image presents both the table of x-y coordinates and the resulting graph. Interestingly, the graph is identical to that of y = -1 / x, showing a hyperbola with branches in the second and fourth quadrants. This example demonstrates how different forms of rational functions can produce the same graph. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 4 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 4TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (-x). The image showcases both the table of x-y coordinates and the resulting graph. Notably, the graph is identical to that of y = 1 / x, displaying a hyperbola with branches in the first and third quadrants. This example further illustrates how different forms of rational functions can produce the same graph. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 5 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 5TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = 1 / (x + 1). The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The graph is a hyperbola with points marked at specific coordinates, illustrating how the addition of a constant in the denominator affects the graph's position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 6 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 6TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (x + 1). The image showcases both the table of x-y coordinates and the resulting graph. The graph displays a hyperbola with labeled points on the curve, illustrating how the negative sign in the numerator and the constant in the denominator affect the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 7 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 7TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = 1 / (-x + 1). The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The graph is a hyperbola with specific points highlighted, illustrating how the negative sign and constant in the denominator affect the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 8 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 8TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (x - 1). The image showcases both the table of x-y coordinates and the resulting graph. The graph features a hyperbola with marked points on its curve, illustrating how the constant in the denominator affects the graph's position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 9 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 9TopicRational Functions DescriptionThis math example illustrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (-x + 1). The image presents both the table of x-y coordinates and the resulting graph. The graph is plotted with points labeled at specific coordinates, demonstrating how the negative signs in both the numerator and denominator affect the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 1 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 1TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 10 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 10TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 11 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 11TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 12 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 12TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 13 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 13TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 14 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 14TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 15 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 15TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 16 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 16TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 17 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 17TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 18 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 18TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 19 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 19TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 2 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 2TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 20 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 20TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 21 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 21TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 22 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 22TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 23 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 23TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 24 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 24TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 25 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 25TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 26 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 26TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 27 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 27TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 28 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 28TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 29 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 29TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 3 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 3TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 30 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 30TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 31 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 31TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 32 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 32TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 33 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 33TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 34 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 34TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 35 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 35TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 36 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 36TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 37 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 37TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 38 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 38TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 39 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 39TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 4 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 4TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 40 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 40TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 5 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 5TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 6 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 6TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 7 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 7TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 8 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 8TopicSpecial Functions |
Polynomial Functions and Equations |
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Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 9 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 9TopicSpecial Functions |
Polynomial Functions and Equations |
