Illustrative Math Alignment: Grade 8 Unit 3

Functions and Volume

Lesson 6: Even More Graphs of Functions

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
Math Example--Rational Concepts--Graphs of Rational Functions: Example 15	Math Example--Rational Concepts--Graphs of Rational Functions: Example 15 Topic Rational Functions Description This example showcases the graph of the rational function y = (x + 4) / ((x + 2)(x - 5)). The graph features vertical asymptotes at x = -2 and x = 5, demonstrating the behavior of the function near these asymptotes. Students are tasked with graphing the function and determining its vertical asymptotes.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 16	Math Example--Rational Concepts--Graphs of Rational Functions: Example 16 Topic Rational Functions Description This example illustrates the graph of the rational function y = (x - 9) / ((x - 1)(x + 3)). The graph features vertical asymptotes at x = -3 and x = 1, showing the function's behavior around these asymptotes. Students are asked to graph the function and identify its vertical asymptotes.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 17	Math Example--Rational Concepts--Graphs of Rational Functions: Example 17 Topic Rational Functions Description This example presents 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. Students are tasked with graphing the function and determining its vertical asymptotes.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 18	Math Example--Rational Concepts--Graphs of Rational Functions: Example 18 Topic Rational Functions Description This example illustrates the graph of the rational function y = (x - 8) / ((x + 3)(x - 3)). The graph features vertical asymptotes at x = -3 and x = 3, highlighted by dashed red lines. Students are asked to graph the function and identify its vertical asymptotes.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 19	Math Example--Rational Concepts--Graphs of Rational Functions: Example 19 Topic Rational Functions Description This example presents the graph of the rational function y = -(x + 1) / (x + 2). The graph features a single vertical asymptote at x = -2, indicated by a dashed red line. Students are tasked with graphing the function and determining its vertical asymptote.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 2	Math Example--Rational Concepts--Graphs of Rational Functions: Example 2 Topic Rational Functions Description This example illustrates the graph of the rational function y = -1 / x. The graph is a hyperbola with vertical and horizontal asymptotes, with the vertical asymptote at x = 0. Students are asked to graph the function and identify its vertical asymptote.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 20	Math Example--Rational Concepts--Graphs of Rational Functions: Example 20 Topic Rational Functions Description This example showcases the graph of the rational function y = -(x - 3) / (x + 4). The graph features a vertical asymptote at x = -4, but it is incorrectly labeled as x = -2. Students are asked to graph the function and identify its vertical asymptote.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 21	Math Example--Rational Concepts--Graphs of Rational Functions: Example 21 Topic Rational Functions Description This example illustrates the graph of the rational function y = -(x - 5) / (x - 4). The graph features a vertical asymptote at x = 4, which is correctly labeled. Students are tasked with graphing the function and determining its vertical asymptote.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 22	Math Example--Rational Concepts--Graphs of Rational Functions: Example 22 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.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 23	Math Example--Rational Concepts--Graphs of Rational Functions: Example 23 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.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 24	Math Example--Rational Concepts--Graphs of Rational Functions: Example 24 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.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 25	Math Example--Rational Concepts--Graphs of Rational Functions: Example 25 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.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 26	Math Example--Rational Concepts--Graphs of Rational Functions: Example 26 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.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 27	Math Example--Rational Concepts--Graphs of Rational Functions: Example 27 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.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 28	Math Example--Rational Concepts--Graphs of Rational Functions: Example 28 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.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 3	Math Example--Rational Concepts--Graphs of Rational Functions: Example 3 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.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 4	Math Example--Rational Concepts--Graphs of Rational Functions: Example 4 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.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 5	Math Example--Rational Concepts--Graphs of Rational Functions: Example 5 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.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 6	Math Example--Rational Concepts--Graphs of Rational Functions: Example 6 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.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 7	Math Example--Rational Concepts--Graphs of Rational Functions: Example 7 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.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 8	Math Example--Rational Concepts--Graphs of Rational Functions: Example 8 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.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 9	Math Example--Rational Concepts--Graphs of Rational Functions: Example 9 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.	Rational Functions and Equations
MATH EXAMPLES--Teacher's Guide: Graphs of Rational Functions	MATH EXAMPLES--Teacher's Guide: Graphs of Rational Functions This Teacher's Guide provides an overview of the 28 worked-out examples that show how to graph Rational Functions. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Rational Functions and Equations
Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 01, Level 1	Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 01, Level 1 This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Graphs of Linear Functions and Slope-Intercept Form
Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 01, Level 2	Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 01, Level 2 This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Graphs of Linear Functions and Slope-Intercept Form
Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 01, Level 3	Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 01, Level 3 This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Graphs of Linear Functions and Slope-Intercept Form
Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 02, Level 1	Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 02, Level 1 This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Graphs of Linear Functions and Slope-Intercept Form
Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 02, Level 2	Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 02, Level 2 This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Graphs of Linear Functions and Slope-Intercept Form
Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 02, Level 3	Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 02, Level 3 This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Graphs of Linear Functions and Slope-Intercept Form
Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 03, Level 1	Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 03, Level 1 This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Graphs of Linear Functions and Slope-Intercept Form
Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 03, Level 2	Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 03, Level 2 This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Graphs of Linear Functions and Slope-Intercept Form
Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 03, Level 3	Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 03, Level 3 This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Graphs of Linear Functions and Slope-Intercept Form
Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 04, Level 1	Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 04, Level 1 This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Graphs of Linear Functions and Slope-Intercept Form
Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 04, Level 2	Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 04, Level 2 This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Graphs of Linear Functions and Slope-Intercept Form
Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 04, Level 3	Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 04, Level 3 This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Graphs of Linear Functions and Slope-Intercept Form
Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 05, Level 1	Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 05, Level 1 This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Graphs of Linear Functions and Slope-Intercept Form
Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 05, Level 2	Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 05, Level 2 This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Graphs of Linear Functions and Slope-Intercept Form
Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 05, Level 3	Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 05, Level 3 This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Graphs of Linear Functions and Slope-Intercept Form
Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 06, Level 1	Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 06, Level 1 This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Graphs of Linear Functions and Slope-Intercept Form
Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 06, Level 2	Paper-and-Pencil Quiz: Graphs of Linear Functions, Quiz 06, Level 2 This is part of a collection of math quizzes on the topic of graphs of linear functions. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Graphs of Linear Functions and Slope-Intercept Form

Illustrative Math Alignment: Grade 8 Unit 3

Functions and Volume

Lesson 6: Even More Graphs of Functions

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