Illustrative Math Alignment: Grade 8 Unit 3

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This 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.

Topic

Exponential Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the exponential function y = -1 * 2-3x. 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 factor in the exponent.

Topic

Exponential Functions

Description

This example demonstrates the creation of a table of x-y coordinates and the graphing of the exponential function y = -4 * 2-3x. 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 negative coefficient, a larger magnitude, and a factor in the exponent.

Topic

Exponential Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the exponential function y = -0.5 * 2x. The image presents both a table of values and a graph, displaying the function's behavior. The table lists x-y coordinates for x values from -2 to 2, with corresponding y values calculated using the given function. This representation helps students visualize an exponential function with a negative fractional coefficient.

Related Resources

Create a Slide Show

Accessibility

Related Resources

Create a Slide Show

Accessibility

Related Resources

Create a Slide Show

Accessibility

Related Resources

Create a Slide Show

Accessibility

Related Resources

Create a Slide Show

Accessibility

Related Resources

Create a Slide Show

Accessibility

Related Resources

Create a Slide Show

Accessibility

Related Resources

Create a Slide Show

Accessibility

Related Resources

Create a Slide Show

Accessibility

Related Resources

Create a Slide Show

Accessibility

Topic

Linear Functions

Description

This example demonstrates how to create a table of x-y coordinates and graph the linear function y = 2x + 4. The image shows both a graph and a table representing this function. The table includes coordinate pairs (0, 4), (1, 6), (2, 8), (3, 10), and (4, 12), illustrating how the y-value increases by 2 for each unit increase in x.

Topic

Linear Functions

Description

This example demonstrates how to create a table of x-y coordinates and graph the linear function y = -x + 6. The image shows both a graph and a table representing this function. The table includes coordinate pairs (0, 6), (1, 5), (2, 4), (3, 3), and (4, 2), illustrating how the y-value decreases by 1 for each unit increase in x.

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = -x - 8. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, -8), (1, -9), (2, -10), (3, -11), and (4, -12), showing how the y-value decreases by 1 for each unit increase in x.

Topic

Linear Functions

Description

This example demonstrates the creation of a table of x-y coordinates and the graphing of the linear function y = -x. The image displays both a graph and a table representing this function. The table includes coordinate pairs (0, 0), (1, -1), (2, -2), (3, -3), and (4, -4), illustrating how the y-value decreases by 1 for each unit increase in x.

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = 0.5x + 4. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, 4), (1, 4.5), (2, 5), (3, 5.5), and (4, 6), showing how the y-value increases by 0.5 for each unit increase in x.

Topic

Linear Functions

Description

This example demonstrates how to create a table of x-y coordinates and graph the linear function y = 0.1x - 5. The image shows both a graph and a table representing this function. The table includes coordinate pairs (0, -5), (1, -4.9), (2, -4.8), (3, -4.7), and (4, -4.6), illustrating how the y-value increases by 0.1 for each unit increase in x.

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = 0.2x. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, 0), (1, 0.2), (2, 0.4), (3, 0.6), and (4, 0.8), showing how the y-value increases by 0.2 for each unit increase in x.

Topic

Linear Functions

Description

This example demonstrates how to create a table of x-y coordinates and graph the linear function y = -0.5x + 7. The image shows both a graph and a table representing this function. The table includes coordinate pairs (0, 7), (1, 6.5), (2, 6), (3, 5.5), and (4, 5), illustrating how the y-value decreases by 0.5 for each unit increase in x.

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = -0.1x - 4. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, -4), (1, -4.1), (2, -4.2), (3, -4.3), and (4, -4.4), showing how the y-value decreases by 0.1 for each unit increase in x.

Topic

Linear Functions

Description

This example demonstrates how to create a table of x-y coordinates and graph the linear function y = -0.6x. The image shows both a graph and a table representing this function. The table includes coordinate pairs (0, 0), (1, -0.6), (2, -1.2), (3, -1.8), and (4, -2.4), illustrating how the y-value decreases by 0.6 for each unit increase in x.

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = 0x. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, 0), (1, 0), (2, 0), (3, 0), and (4, 0), showing how the y-value remains constant at 0 for all values of x.

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = 3x - 2. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, -2), (1, 1), (2, 4), (3, 7), and (4, 10), showing how the y-value increases by 3 for each unit increase in x.

Topic

Linear Functions

Description

This example demonstrates how to create a table of x-y coordinates and graph the linear function y = 0x - 6. The image shows both a graph and a table representing this function. The table includes coordinate pairs (0, -6), (1, -6), (2, -6), (3, -6), and (4, -6), illustrating how the y-value remains constant at -6 for all values of x.

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = 0 * x + 4. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, 4), (1, 4), (2, 4), (3, 4), and (4, 4), showing how the y-value remains constant at 4 for all values of x.