Illustrative Math Alignment: Grade 8 Unit 3

Topic

Rational Functions

Description

This example presents the graph of the rational function y = -(x + 2) / ((x + 4)(x + 1)). The graph features vertical asymptotes at x = -4 and x = -1. Students are asked to graph the function and identify its vertical asymptotes.

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = -(x - 4) / ((x + 5)(x + 2)). The graph features vertical asymptotes at x = -5 and x = -2. Students are tasked with graphing the function and determining its vertical asymptotes.

Topic

Rational Functions

Description

This example showcases the graph of the rational function y = -(x + 2) / ((x - 3)(x + 7)). The graph features vertical asymptotes at x = -7 and x = 3. Students are asked to graph the function and identify its vertical asymptotes.

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = -(x + 1) / ((x + 2)(x - 8)). The graph features vertical asymptotes at x = -2 and x = 8. Students are tasked with graphing the function and determining its vertical asymptotes.

Topic

Rational Functions

Description

This example showcases the graph of the rational function y = -(x - 4) / ((x - 3)(x + 2)). The graph features vertical asymptotes at x = -2 and x = 3. Students are asked to graph the function and identify its vertical asymptotes.

Topic

Rational Functions

Description

This example presents the graph of the rational function y = -(x - 3) / ((x + 3)(x - 1)). The graph features vertical asymptotes at x = -3 and x = 1. Students are tasked with graphing the function and determining its vertical asymptotes.

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = -(x - 1) / ((x - 2)(x - 3)). The graph features vertical asymptotes at x = 2 and x = 3, marked with dashed red lines on the coordinate plane. Students are asked to graph the function and identify its vertical asymptotes.

Topic

Rational Functions

Description

This example showcases the graph of the rational function y = 1 / (x + 2). The graph is a hyperbola with a vertical asymptote at x = -2. Students are tasked with graphing the function and determining its vertical asymptote.

Topic

Rational Functions

Description

This example presents the graph of the rational function y = 1 / (x - 4). The graph is a hyperbola with a vertical asymptote at x = 4. Students are asked to graph the function and identify its vertical asymptote.

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = 1 / (5x + 3). The graph features a vertical asymptote at x = -0.6, indicated by a dashed red line. Students are tasked with graphing the function and determining its vertical asymptote.

Topic

Rational Functions

Description

This example demonstrates the graph of the rational function y = -1 / (6x + 2). The graph features a vertical asymptote at x = -1/3, shown with a dashed red line on the grid. Students are asked to graph the function and identify its vertical asymptote.

Topic

Rational Functions

Description

This example showcases the graph of the rational function y = 1 / (5x - 7). The graph features a vertical asymptote at x = 1.4, marked by a dashed red line on the grid. Students are tasked with graphing the function and determining its vertical asymptote.

Topic

Rational Functions

Description

This example presents the graph of the rational function y = 1 / (-9x + 3). The graph is plotted on a grid with a vertical asymptote at x = 1/3, marked by a dashed red line. Students are asked to graph the function and identify its vertical asymptote.

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = (x + 3) / (x + 2). The graph features a vertical asymptote at x = -2 and shows two branches, one in the second quadrant and one in the fourth quadrant. Students are tasked with graphing the function and determining its vertical asymptote.

This Teacher's Guide provides an overview of the 32 worked-out examples that show how to find the equation of a line parallel or perpendicular to a given line and through a given point.

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This Teacher's Guide provides an overview of the 28 worked-out examples that show how to graph Rational Functions.

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To see resources related to this topic click on the Related Resources tab above.

August 2013. In this issue we look at Diana Nyad's remarkable swim from Cuba to Florida. It becomes an opportunity to explore Average Speed.

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The relationship between slope and grade in cycling is explored. Go on a tour of Italy through the mountains of Tuscany and apply students' understanding of slope. Note: The download for this resources is the Promethean Flipchart.

To access the full video: [Algebra Applications: Linear Functions, Segment 2: Cycling]: https://www.media4math.com/library/video-algebra-applications-linear-functions-segment-2-cycling

This video includes a Video Transcript: [Algebra Applications: Linear Functions, Segment 2: Cycling]: https://www.media4math.com/library/video-transcript-algebra-applications-linear-functions-segment-2-cycling

Exercise needs to become a consistent part of everyone's lifestyle. In particular, aerobic exercises, which vigorously exerts the heart, is an important form of exercise. The maximum heart rate from aerobic exercise is a linear function dependent on age. Students are asked to develop a data table based on the function. Note: The download for this resources is the Promethean Flipchart.

To access the full video: [Algebra Applications: Linear Functions, Segment 4: Exercise]: https://www.media4math.com/library/video-algebra-applications-linear-functions-segment-4-exercise

The potential for oil exploration in the controversial Alaska National Wildlife Refuge (ANWR) sets the scene for this problem. A linear regression of oil consumption data over the past 25 years reveals an interesting pattern. How could new oil fields like ANWR help in breaking our dependence on foreign oil? Note: The download for this resources is the Promethean Flipchart.

To access the full video [Algebra Applications: Linear Functions, Segment 3: Oil Exploration]: https://www.media4math.com/library/video-algebra-applications-linear-functions-segment-3-oil-exploration

In this program, internationally acclaimed mathematics educator Dr. Monica Neagoy, explores the nature of linear functions through the use TI graphing calculators. Examples ranging from air travel, construction, engineering, and space travel provide real-world examples for discovering algebraic concepts. All examples are solved algebraically and then reinforced through the use of the TI-Nspire. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series. Concepts explored: Standard form, slope-intercept form, point-slope form, solving linear equations Note: The download for this resources is the Promethean Flipchart.

This video includes a Teacher's Guide: https://www.media4math.com/library/algebra-nspirations-teachers-guide-linear-functions

This video begins with the historical invention of logarithms that forever changed the world of computation—until the advent of calculators more than 300 years later. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, it proceeds to derive the properties of logs, examine logarithmic functions and graphs, and finally explore the well-known Richter logarithmic scale. Concepts explored: functions and inverse functions, logarithms, exponential functions, logarithmic functions Note: The download for this resources is the Promethean Flipchart.

To access the full video: [Algebra Nspirations: Logarithms and Logarithmic Functions]: https://www.media4math.com/library/algebra-nspirations-logarithms-and-logarithmic-functions

In this set of Quizlet flash cards test understanding of the point-slope form.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

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In this set of Quizlet flash cards test understanding of the slope-intercept form.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

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This is part of a collection of self-scoring interactive math quizzes on a variety of topics.

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In this TI-84 tutorial we show how to graph linear functions and trace their coordinates. Note: The download is a PPT file.

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

This is the transcript for the video of same title. Video contents: In this program, internationally acclaimed mathematics educator Dr. Monica Neagoy, explores the nature of linear functions through the use TI graphing calculators. Examples ranging from air travel, construction, engineering, and space travel provide real-world examples for discovering algebraic concepts. All examples are solved algebraically and then reinforced through the use of the TI-Nspire. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series. Concepts explored: Standard form, slope-intercept form, point-slope form, solving linear equations

This is the transcript for the video of same title. Video contents: In this Investigation we look at linear models for objects moving at a constant speed.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript for the video of same title. Video contents: In this Investigation we look at a linear regression for carbon dioxide emission data.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript that goes with the video segment entitled Video: Linear Functions: Negative Slope, Negative y-Intercept.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript that goes with the video segment entitled Video: Linear Functions: Negative Slope, Positive y-Intercept.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript that goes with the video segment entitled Video: Linear Functions: Negative Slope, Zero y-Intercept.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript that goes with the video segment entitled Video: Linear Functions: Positive Slope, Negative y-Intercept.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript that goes with the video segment entitled Video: Linear Functions: Positive Slope, Positive y-Intercept.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript that goes with the video segment entitled Video: Linear Functions: Positive Slope, Zero y-Intercept.

To see the complete collection of video transcriptsy, click on this link.

Learn the basics of decreasing functions. Graphical and algebraic representations of decreasing functions are shown, as well as examples of such functions.

Learn the basics of increasing functions. Graphical and algebraic representations of increasing functions are shown, as well as examples of such functions.

Topic

Linear Functions

Description

The video covers linear functions with positive slope and positive y-intercept. It explains the slope-intercept form y = mx + b, where m is the slope indicating steepness, calculated as rise over run, and b is the y-intercept, the y-value at the point where the line intersects the y-axis. For this function, the slope is 2, and the y-intercept is 2. The graph is demonstrated by moving up two units and one to the right, confirming the slope. The y-intercept at point (0, 2) is also identified.

Topic

Linear Functions

Description

This video discusses linear functions with positive slope and negative y-intercept. It reviews the slope-intercept form y = mx + b. The slope measures steepness as the ratio of rise to run, and the y-intercept is the point where the line meets the y-axis. Here, the slope is 2, and the y-intercept is -3, evidenced by the graph where the line starts at (0, -3) and rises two units for every unit right.

Topic

Linear Functions

Description

The video explains linear functions with a positive slope and zero y-intercept. In slope-intercept form y = mx + b, the slope, m, represents the steepness, while the y-intercept, b, is zero. The slope of 2 is confirmed by graphing: moving up two units and one to the right. The line passes through the origin, demonstrating a y-intercept of 0.

Topic

Linear Functions

Description

This video focuses on linear functions with a negative slope and positive y-intercept. Using the slope-intercept form y = mx + b, the slope of -3 indicates a downward slope, and the y-intercept of 2 is the point (0, 2). Graphically, moving down three units and one unit to the left confirms the slope of -3.

Topic

Linear Functions

Description

The video covers linear functions with a negative slope and negative y-intercept. It explains the slope-intercept form y = mx + b, with a slope of -3 and a y-intercept of -2 at (0, -2). The graph shows a downward slope with three units down and one unit left, confirming the slope.

Topic

Linear Functions

Description

This video addresses linear functions with a negative slope and zero y-intercept. In slope-intercept form y = mx + b, the slope is -3, indicating a downward trend. The line passes through the origin, confirming the zero y-intercept, and graphing demonstrates the negative slope.

Topic

Linear Functions

Description

Applies linear functions to cycling, calculating hill grades and distances using slope formulas and graphing.

Linear functions are fundamental in understanding mathematical relationships between two variables. The video demonstrates their application in real-life scenarios, enhancing comprehension of key concepts like slope, intercepts, and graphical representation. This foundational knowledge prepares students for more advanced mathematical topics.

Topic

Linear Functions