Illustrative Math Alignment: Grade 8 Unit 3
Functions and Volume
Lesson 3: Equations for Functions
Use the following Media4Math resources with this Illustrative Math lesson.
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 10 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 10TopicExponential Functions DescriptionThis example demonstrates the creation of a table of x-y coordinates and the graphing of the exponential function y = 1 * 2-0.3x. The image provides both a table of values and a graph plotted on a coordinate plane, with points labeled for x values ranging from -2 to 2. This representation helps students visualize the behavior of a decreasing exponential function with a fractional exponent. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 11 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 11TopicExponential Functions DescriptionThis example illustrates the process of creating a table of x-y coordinates and graphing the exponential function y = -0.4 * 2-0.6x. The image presents both a table of values and a graph plotted on a coordinate plane, with points labeled for x values from -2 to 2. This representation helps students visualize the behavior of a decreasing exponential function with a negative coefficient and a fractional exponent. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 12 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 12TopicExponential Functions DescriptionThis example demonstrates the creation of a table of x-y coordinates and the graphing of the exponential function y = -0.5 * 2-x. The image provides both a table of values and a graph plotted on a coordinate plane, with points labeled for x values ranging from -2 to 2. This representation helps students visualize the behavior of a decreasing exponential function with a negative coefficient and a negative exponent. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 13 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 13TopicExponential Functions DescriptionThis example illustrates the process of creating a table of x-y coordinates and graphing the exponential function y = -1 * 2-0.5x. The image presents both a table of values and a graph plotted on a coordinate plane, with points labeled for x values from -2 to 2. This representation helps students visualize the behavior of an increasing exponential function with a negative coefficient and a fractional negative exponent. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 14 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 14TopicExponential Functions DescriptionThis example demonstrates the creation of a table of x-y coordinates and the graphing of the exponential function y = 0.5 * 2x. The image provides both a table of values and a graph plotted on a coordinate plane, with points labeled for x values ranging from -2 to 2. This representation helps students visualize the behavior of an increasing exponential function with a fractional coefficient. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 15 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 15TopicExponential Functions DescriptionThis example illustrates the process of creating a table of x-y coordinates and graphing the exponential function y = 1 * 20.7x. The image presents both a table of values and a graph plotted on a coordinate plane, with points labeled for x values from -2 to 2. This representation helps students visualize the behavior of an increasing exponential function with a fractional positive exponent. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 16 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 16TopicExponential Functions DescriptionThis example demonstrates the creation of a table of x-y coordinates and the graphing of the exponential function y = 0.4 * 20.9x. The image provides both a table of values and a graph plotted on a Cartesian plane, with points labeled for x values ranging from -2 to 2. This representation helps students visualize the behavior of an increasing exponential function with a fractional coefficient and a fractional exponent. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 17 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 17TopicExponential Functions DescriptionThis example illustrates the process of creating a table of x-y coordinates and graphing the exponential function y = 0.6 * 2-x. The image presents both a table of values and a graph plotted on a coordinate plane, with points labeled for x values from -2 to 2. This representation helps students visualize the behavior of a decreasing exponential function with a fractional coefficient and a negative exponent. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 18 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 18TopicExponential Functions DescriptionThis example demonstrates the creation of a table of x-y coordinates and the graphing of the exponential function y = -1 * 20.8x. The image provides both a table of values and a graph plotted on a coordinate plane, with points labeled for x values ranging from -2 to 2. This representation helps students visualize the behavior of a decreasing exponential function with a negative coefficient and a fractional positive exponent. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 19 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 19TopicExponential Functions DescriptionThis example illustrates the process of creating a table of x-y coordinates and graphing the exponential function y = 1 * 10x. The image presents both a table of values and a graph plotted on a coordinate plane, with points labeled for x values from -2 to 2. This representation helps students visualize the behavior of an increasing exponential function with a base of 10. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 2 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 2TopicExponential Functions DescriptionThis example presents the exponential function y = 4 * 2x through a table of x-y coordinates and its corresponding graph. The table shows five key points: (-2, 1), (-1, 2), (0, 4), (1, 8), and (2, 16). These points are then plotted on a graph, demonstrating how the function grows exponentially as x increases. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 20 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 20TopicExponential Functions DescriptionThis example demonstrates the creation of a table of x-y coordinates and the graphing of the exponential function y = 4 * 10x. The image provides both a table of values and a graph plotted on a coordinate plane, with points labeled for x values ranging from -2 to 2. This representation helps students visualize the behavior of an increasing exponential function with a coefficient greater than 1 and a base of 10. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 21 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 21TopicExponential Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the exponential function y = 1 * 102x. The image displays both a graph and a corresponding table, illustrating the rapid growth of this function. The table includes key points such as (-2, 0.0001), (-1, 0.01), (0, 1), (1, 100), and (2, 10,000), demonstrating how quickly the y-values increase as x increases. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 22 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 22TopicExponential Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the exponential function y = 3 * 103x. The image showcases both a graph and a corresponding table, highlighting the extremely rapid growth of this function. The table includes key points such as (-2, 3 * 10-6), (-1, 0.003), (0, 3), (1, 3000), and (2, 3 * 106), illustrating the dramatic increase in y-values as x increases. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 23 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 23TopicExponential Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the exponential function y = -1 * 10-x. The image displays both a graph and a corresponding table, illustrating the behavior of this negative exponential function. The table includes key points such as (-2, -100), (-1, -10), (0, -1), (1, -0.1), and (2, -0.01), demonstrating how the y-values approach zero as x increases. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 24 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 24TopicExponential Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the exponential function y = -3 * 10-x. The image showcases both a graph and a corresponding table, highlighting the behavior of this negative exponential function with a coefficient. The table includes key points such as (-2, -300), (-1, -30), (0, -3), (1, -0.3), and (2, -0.03), illustrating how the y-values approach zero from the negative side as x increases. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 25 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 25TopicExponential Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the exponential function y = -1 * 10-2x. The image displays both a graph and a corresponding table, illustrating the behavior of this negative exponential function with a doubled exponent. The table includes key points such as (-2, -10000), (-1, -100), (0, -1), (1, -0.01), and (2, -1 * 10-4), demonstrating how rapidly the y-values approach zero from the negative side as x increases. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 26 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 26TopicExponential Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the exponential function y = -3 * 10-2x. The image showcases both a graph and a corresponding table, highlighting the behavior of this negative exponential function with a coefficient and a doubled exponent. The table includes key points such as (-2, -30000), (-1, -300), (0, -3), (1, -0.03), and (2, -3 * 10-4), illustrating how rapidly the y-values approach zero from the negative side as x increases. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 27 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 27TopicExponential Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the exponential function y = -0.4 * 10x. The image displays both a graph and a corresponding table, illustrating the behavior of this negative exponential function with a fractional coefficient. The table includes key points such as (-2, -0.004), (-1, -0.04), (0, -0.4), (1, -4), and (2, -40), demonstrating how the y-values decrease rapidly in the negative direction as x increases. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 28 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 28TopicExponential Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the exponential function y = 1 * 100.5x. The image showcases both a graph and a corresponding table, highlighting the behavior of this exponential function with a fractional exponent. The table includes key points such as (-2, 0.1), (-1, 0.316), (0, 1), (1, 3.162), and (2, 10), illustrating how the y-values increase at a slower rate compared to a standard exponential function. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 29 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 29TopicExponential Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the exponential function y = -0.5 * 10-0.3x. The image displays both a graph and a corresponding table, illustrating the behavior of this negative exponential function with a fractional coefficient and a negative fractional exponent. The table includes key points such as (-2, -1.99), (-1, -0.998), (0, -0.5), (1, -0.251), and (2, -0.126), demonstrating how the y-values approach zero from the negative side as x increases. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 3 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 3TopicExponential Functions DescriptionThis example showcases the exponential function y = 1 * 23x through a table of x-y coordinates and its corresponding graph. The table presents five key points: (-2, 0.02), (-1, 0.13), (0, 1), (1, 8), and (2, 64). These points are then plotted on a graph, illustrating the rapid growth of this function as x increases. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 30 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 30TopicExponential Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the exponential function y = -0.6 * 10-x. The image showcases both a graph and a corresponding table, highlighting the behavior of this negative exponential function with a fractional coefficient and a negative exponent. The table includes key points such as (-2, -60), (-1, -6), (0, -0.6), (1, -0.06), and (2, -0.006), illustrating how rapidly the y-values approach zero from the negative side as x increases. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 31 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 31TopicExponential Functions DescriptionThis math example demonstrates the exponential function y = -1 * 10-0.7x in both tabular and graphical form. The table provides x-y coordinates for x values ranging from -2 to 2, showing how the function's output changes as x increases. The corresponding graph visually represents this relationship, illustrating the characteristic shape of an exponential decay function. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 32 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 32TopicExponential Functions DescriptionThis math example illustrates the exponential function y = -0.4 * 10x through both a table of values and a graph. The table presents x-y coordinates for x values from -2 to 2, demonstrating how the function's output changes rapidly as x increases. The accompanying graph provides a visual representation of this exponential growth function, highlighting its distinctive shape and behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 33 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 33TopicExponential Functions DescriptionThis math example showcases the exponential function y = 1 * 100.6x through a table of x-y coordinates and a corresponding graph. The table lists values for x ranging from -2 to 2, illustrating how the function's output changes as x increases. The graph provides a visual representation of this exponential growth function, emphasizing its characteristic shape and behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 34 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 34TopicExponential Functions DescriptionThis math example presents the exponential function y = 0.6 * 100.8x through both a table of x-y coordinates and a graph. The table provides values for x ranging from -2 to 2, demonstrating how the function's output changes as x increases. The accompanying graph offers a visual representation of this exponential growth function, highlighting its distinctive shape and behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 35 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 35TopicExponential Functions DescriptionThis math example illustrates the exponential function y = 0.8 * 10-x through a table of x-y coordinates and a corresponding graph. The table lists values for x ranging from -2 to 2, showing how the function's output changes as x increases. The graph provides a visual representation of this exponential decay function, emphasizing its characteristic shape and behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 36 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 36TopicExponential Functions DescriptionThis math example illustrates the exponential function y = -1 * 10-0.3x through both a table of values and a graph. The table presents x-y coordinates for x values from -2 to 2, demonstrating how the function's output changes as x increases. The accompanying graph provides a visual representation of this exponential decay function with a negative coefficient, highlighting its distinctive shape and behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 37 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 37TopicExponential Functions DescriptionThis math example presents the exponential function y = 1 * ex through both a table of x-y coordinates and a graph. The table provides values for x ranging from -2 to 2, demonstrating how the function's output changes as x increases. The accompanying graph offers a visual representation of this natural exponential function, highlighting its characteristic shape and behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 38 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 38TopicExponential Functions DescriptionThis math example illustrates the exponential function y = 5 * ex through a table of x-y coordinates and a corresponding graph. The table lists values for x ranging from -2 to 2, showing how the function's output changes as x increases. The graph provides a visual representation of this scaled natural exponential function, emphasizing its characteristic shape and behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 39 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 39TopicExponential Functions DescriptionThis math example showcases the exponential function y = 1 * e3x through a table of x-y coordinates and a corresponding graph. The table lists values for x ranging from -2 to 2, illustrating how the function's output changes rapidly as x increases. The graph provides a visual representation of this exponential growth function with a modified exponent, emphasizing its steep growth curve and behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 4 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 4TopicExponential Functions DescriptionThis example demonstrates how to create a table of x-y coordinates and graph the exponential function y = 3 * 22x. The image provides a visual representation of the function, showing both a table of coordinates and a graph plotted on a coordinate plane. The table lists x-y coordinates for x values ranging from -2 to 2, with corresponding y values calculated using the given function. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 40 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 40TopicExponential Functions DescriptionThis math example illustrates the exponential function y = 6 * e2x through both a table of values and a graph. The table presents x-y coordinates for x values from -2 to 2, demonstrating the rapid growth of this function as x increases. The accompanying graph provides a visual representation of this exponential growth function, highlighting its steep curve and behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 41 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 41TopicExponential Functions DescriptionThis math example showcases the exponential function y = -1 * e-x through a table of x-y coordinates and a corresponding graph. The table lists values for x ranging from -2 to 2, illustrating how the function's output changes as x increases. The graph provides a visual representation of this exponential decay function with a negative coefficient, emphasizing its unique shape and behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 42 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 42TopicExponential Functions DescriptionThis math example illustrates the exponential function y = -7 * e-x through both a table of values and a graph. The table presents x-y coordinates for x values from -2 to 2, demonstrating how the function's output changes as x increases. The accompanying graph provides a visual representation of this exponential decay function with a negative coefficient, highlighting its distinctive shape and behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 43 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 43TopicExponential Functions DescriptionThis math example showcases the exponential function y = -1 * e-2x through a table of x-y coordinates and a corresponding graph. The table lists values for x ranging from -2 to 2, illustrating how the function's output changes rapidly as x increases. The graph provides a visual representation of this exponential growth function with a negative coefficient, emphasizing its unique shape and behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 44 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 44TopicExponential Functions DescriptionThis math example illustrates the exponential function y = -5 * e-3x through both a table of values and a graph. The table presents x-y coordinates for x values from -2 to 2, demonstrating the extremely rapid change in the function's output as x increases. The accompanying graph provides a visual representation of this exponential growth function with a negative coefficient and tripled exponent, highlighting its steep curve and unique behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 45 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 45TopicExponential Functions DescriptionThis example showcases the exponential function y = -0.5 * ex through a graph and table of x-y coordinates. The table provides points (-2, -0.068), (-1, -0.184), (0, -0.5), (1, -1.36), and (2, -3.69), which are plotted on the accompanying graph. Students are tasked with creating this table and graph to visualize the function's behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 46 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 46TopicExponential Functions DescriptionThis example showcases the exponential function y = 1 * e-0.5x through a graph and table of x-y coordinates. The table provides points (-2, 2.718), (-1, 1.648), (0, 1), (1, 0.607), and (2, 0.368), which are plotted on the accompanying graph. Students are tasked with creating this table and graph to visualize the function's behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 47 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 47TopicExponential Functions DescriptionThis example illustrates the exponential function y = -0.6 * e-0.7x through a graph and table of x-y coordinates. The table provides points (-2, -2.433), (-1, -1.208), (0, -0.6), (1, -0.298), and (2, -0.148), which are plotted on the accompanying graph. Students are challenged to create this table and graph to visualize the function's behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 48 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 48TopicExponential Functions DescriptionThis example presents the exponential function y = -0.5 * e-x through a graph and table of x-y coordinates. The table provides points (-2, -3.695), (-1, -1.359), (0, -0.5), (1, -0.184), and (2, -0.068), which are plotted on the accompanying graph. Students are tasked with creating this table and graph to visualize the function's behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 49 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 49TopicExponential Functions DescriptionThis example illustrates the exponential function y = -1 * e-0.6x through a graph and table of x-y coordinates. The table provides points (-2, -3.32), (-1, -1.822), (0, -1), (1, -0.549), and (2, -0.301), which are plotted on the accompanying graph. Students are challenged to create this table and graph to visualize the function's behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 5 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 5TopicExponential Functions DescriptionThis example illustrates the process of creating a table of x-y coordinates and graphing the exponential function y = -1 * 2-x. The image presents both a table of values and a graph plotted on a coordinate plane, with points labeled for x values from -2 to 2. This representation helps students visualize the behavior of a decreasing exponential function with a negative coefficient. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 50 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 50TopicExponential Functions DescriptionThis example showcases the exponential function y = 0.5 * ex through a graph and table of x-y coordinates. The table provides points (-2, 0.068), (-1, 0.184), (0, 0.5), (1, 1.359), and (2, 3.695), which are plotted on the accompanying graph. Students are tasked with creating this table and graph to visualize the function's behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 51 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 51TopicExponential Functions DescriptionThis example illustrates the exponential function y = e0.6x through a graph and table of x-y coordinates. The table provides points (-2, -0.602), (-1, -1.098), (0, -2), (1, -3.644), and (2, -6.64), which are plotted on the accompanying graph. Students are challenged to create this table and graph to visualize the function's behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 52 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 52TopicExponential Functions DescriptionThis example showcases the exponential function y = 0.6 * e0.7x through a graph and table of x-y coordinates. The table provides points (-2, 0.148), (-1, 0.298), (0, 0.6), (1, 1.208), and (2, 2.433), which are plotted on the accompanying graph. Students are tasked with creating this table and graph to visualize the function's behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 53 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 53TopicExponential Functions DescriptionThis example illustrates the exponential function y = 0.7 * e-x through a graph and table of x-y coordinates. The table provides points (-2, 5.172), (-1, 1.903), (0, 0.7), (1, 0.258), and (2, 0.095), which are plotted on the accompanying graph showing a decreasing curve. Students are challenged to create this table and graph to visualize the function's behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 54 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 54TopicExponential Functions DescriptionThis example presents the exponential function y = -1 * e0.6x through a graph and table of x-y coordinates. The table provides points (-2, -0.301), (-1, -0.549), (0, -1), (1, -1.822), and (2, -3.32), which are plotted on the accompanying graph showing a decreasing curve. Students are tasked with creating this table and graph to visualize the function's behavior. |
Graphs of Exponential and Logarithmic Functions |
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Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 6 | Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 6TopicExponential Functions DescriptionThis example demonstrates the creation of a table of x-y coordinates and the graphing of the exponential function y = -3 * 2-x. The image provides both a table of values and a graph plotted on a coordinate plane, with points labeled for x values ranging from -2 to 2. This representation helps students visualize the behavior of a decreasing exponential function with a negative coefficient and a larger magnitude. |
Graphs of Exponential and Logarithmic Functions |
