Illustrative Math Alignment: Grade 8 Unit 3

Functions and Volume

Lesson 10: Piecewise Linear Functions

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
INSTRUCTIONAL RESOURCE: Desmos Tutorial: Matching Coordinates to Absolute Value Functions	INSTRUCTIONAL RESOURCE: Desmos Tutorial: Matching Coordinates to Absolute Value Functions In this Slide Show, use the Desmos graphing calculator to explore absolute value functions. To see the complete collection of Desmos Resources click on this link. Note: The download is a PPT file. This is part of a collection of Desmos tutorials on a variety of math topics. To see the complete collection of these resources, click on this link. Library of Instructional Resources To see the complete library of Instructional Resources , click on this link.	Special Functions
INSTRUCTIONAL RESOURCE: Desmos Tutorial: Matching Coordinates to Linear Functions	INSTRUCTIONAL RESOURCE: Desmos Tutorial: Matching Coordinates to Linear Functions In this Slide Show, use the Desmos graphing calculator to explore linear functions. To see the complete collection of Desmos Resources click on this link. Note: The download is a PPT file. This is part of a collection of Desmos tutorials on a variety of math topics. To see the complete collection of these resources, click on this link. Library of Instructional Resources To see the complete library of Instructional Resources , click on this link.	Applications of Linear Functions
INSTRUCTIONAL RESOURCE: Tutorial: Graphing Linear Functions	INSTRUCTIONAL RESOURCE: Tutorial: Graphing Linear Functions In this Slide Show, learn about graphs of linear functions. This is part of a collection of tutorials on a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file. Library of Instructional Resources To see the complete library of Instructional Resources , click on this link.	Applications of Linear Functions
INSTRUCTIONAL RESOURCE: Tutorial: Linear Function Models	INSTRUCTIONAL RESOURCE: Tutorial: Linear Function Models In this Slide Show, learn about linear function models. This is part of a collection of tutorials on a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file. Library of Instructional Resources To see the complete library of Instructional Resources , click on this link.	Applications of Linear Functions
INSTRUCTIONAL RESOURCE: Math Examples 12	INSTRUCTIONAL RESOURCE: Math Examples--Equations of Parallel and Perpendicular Lines The complete set of 32 examples that make up this set of tutorials. This is part of a collection of math examples for a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file. Library of Instructional Resources To see the complete library of Instructional Resources , click on this link.	Applications of Linear Functions and Graphs of Linear Functions
INSTRUCTIONAL RESOURCE: Math Examples 19	INSTRUCTIONAL RESOURCE: Math Examples--Graphing Linear Functions in Slope-Intercept Form The complete set of 13 examples that make up this set of tutorials. This is part of a collection of math examples for a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file. Library of Instructional Resources To see the complete library of Instructional Resources , click on this link.	Applications of Linear Functions and Graphs of Linear Functions
INSTRUCTIONAL RESOURCE: Math Examples 23	INSTRUCTIONAL RESOURCE: Math Examples--Graphs of Rational Functions The complete set of 28 examples that make up this set of tutorials. This is part of a collection of math examples for a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file. Library of Instructional Resources To see the complete library of Instructional Resources , click on this link.	Rational Functions and Equations
INSTRUCTIONAL RESOURCE: Math Examples 35	INSTRUCTIONAL RESOURCE: Math Examples--Parallel and Perpendicular Lines This set of tutorials provides 32examples that involve finding the equation of a line parallel or perpendicular to a given line and through a given point. This is part of a collection of math examples for a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file. Library of Instructional Resources To see the complete library of Instructional Resources , click on this link.	Applications of Linear Functions and Graphs of Linear Functions
INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Graphs of Absolute Value Functions	In this Slide Show, absolute value functions are graphed, including graphs centered at the origin, graphs displaced along the x-axis, and graphs displaced along the y-axis. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.	Special Functions
INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Graphs of Inequalities	In this Slide Show, the Graph Window is used to graph linear inequalities. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.	Inequalities and Applications of Linear Functions
INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Graphs of Inequalities with Sliders	In this Slide Show, the Graph Window is used to graph inequalities using sliders. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.	Inequalities and Applications of Linear Functions
INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Graphs of Linear Functions	In this Slide Show, linear functions are graphed. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.	Applications of Linear Functions
INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Graphs of Quadratic Functions in Standard Form with Sliders	In this Slide Show, learn how to graph quadratic functions in standard form using sliders for the values of a, b, and c. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.	Applications of Quadratic Functions and Graphs of Quadratic Functions
INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Graphs of Quadratic Functions in Vertex Form with Sliders	In this Slide Show, learn how to graph quadratic functions in vertex form using sliders for the values of h and k. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.	Applications of Quadratic Functions and Graphs of Quadratic Functions
INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Parallel and Perpendicular Lines	In this Slide Show, explore the properties of parallel and perpendicular lines. Use a slider to define the slope and then graph parallel and perpendicular lines linked to this slider.	Parallel Lines and Perpendicular Lines
INSTRUCTIONAL RESOURCE: Nspire App Tutorial: The Perpendicular Bisectors of a Triangle	In this Slide Show, we show how to construct the perpendicular bisectors of the three sides of a triangle to show they intersect at a single point. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.	Definition of a Triangle and Geometric Constructions with Triangles
Instructional Resource: TI-Nspire Activity: Exploring the Ratio of Circumference to Radius as a Linear Function	In this TI-Nspire Activity, use the Geometry and Graphing Tools to explore the ratio of Circumference to Radius as a linear function. Note: The Preview is a Google Slide Show and the download is a PPT. Subscribers to Media4Math can download resources. To see the complete collection of TI graphing calculator resources, click on this Link.	Applications of Linear Functions, Applications of Circles and Geometric Constructions with Circles
INSTRUCTIONAL RESOURCE: TI-Nspire CX Activity: Graphs of Quadratic Functions	In this Slide Show, learn how to graph quadratic functions in standard form using the TI-Nspire CX. Note: The download is a PPT file.	Applications of Quadratic Functions and Graphs of Quadratic Functions
Instructional Resource: Tutorial: What Are Piecewise Functions?	Instructional Resource: Tutorial: What Are Piecewise Functions? In this tutorial students learn about piecewise functions and their properties. —Press PREVIEW to see the tutorial—	Special Functions
Interactive Crossword Puzzle--Parallel and Perpendicular Lines	Interactive Crossword Puzzle--Parallel and Perpendicular Lines This interactive crossword puzzle tests knowledge of key terms on the topic of the graphs of Parallel and Perpendicular Lines. This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide. Related Resources To see additional resources on this topic, click on the Related Resources tab.	Parallel Lines and Perpendicular Lines
Interactive Math Game--Algebra Jeopardy: Linear Functions	Interactive Math Game--Algebra Jeopardy: Linear Functions Use this Jeopardy-style math game to review linear functions. This Jeopardy game has a bank of hundreds of questions for thousands of unique game experiences. To see the complete set of Math Games and Puzzles, click on this link. This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide. Related Resources To see additional resources on this topic, click on the Related Resources tab.	Graphs of Linear Functions and Slope-Intercept Form
Interactive Math Game--DragNDrop--Equations of Parallel Lines	Interactive Math Game--DragNDrop Math--Equations of Parallel Lines In this drag-and-drop game, match the linear equation with the equation of a parallel line through a given point. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format. This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide. Related Resources To see additional resources on this topic, click on the Related Resources tab.	Slope and Slope-Intercept Form
Interactive Math Game--DragNDrop--Equations of Perpendicular Lines	Interactive Math Game--DragNDrop Math--Equations of Perpendicular Lines In this drag-and-drop game, match the linear equation with the equation of a perpendicular line through a given point. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format. This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide. Related Resources To see additional resources on this topic, click on the Related Resources tab.	Slope and Slope-Intercept Form
Interactive Math Game--DragNDrop--Evaluating Linear Functions	Interactive Math Game--DragNDrop Math--Evaluating Linear Functions In this drag-and-drop game, match f(x) with f(a) for a given value of a. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format. This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide. Related Resources To see additional resources on this topic, click on the Related Resources tab.	Applications of Linear Functions
Interactive Math Game--Equation Burst: Linear Functions	Interactive Math Game--Equation Burst: Linear Functions Use this math game to review linear functions in slope-intercept form. This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide. Related Resources To see additional resources on this topic, click on the Related Resources tab.	Slope-Intercept Form
Math Example--Graphical Solutions to Rational Equations--Example 1	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 10	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 2	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 3	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 4	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 5	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 6	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 7	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 8	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 9	This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Create a Slide Show Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: Accessibility This resource can also be used with a screen reader.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 1	Math Example--Rational Concepts--Graphs of Rational Functions: Example 1 Topic Rational Functions Description This example demonstrates the graph of the rational function y = 1 / x. The graph is a hyperbola with vertical and horizontal asymptotes, with the vertical asymptote occurring at x = 0. 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 10	Math Example--Rational Concepts--Graphs of Rational Functions: Example 10 Topic Rational Functions Description This example showcases the graph of the rational function y = (x - 5) / (x + 4). The graph features a vertical asymptote at x = -4 and displays two branches, one in the first quadrant and one in the third quadrant. 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 11	Math Example--Rational Concepts--Graphs of Rational Functions: Example 11 Topic Rational Functions Description This example showcases the graph of the rational function y = (x - 1) / (x - 3). The graph features a vertical asymptote at x = 3 and displays two distinct branches, one in the first quadrant and another in the third quadrant. Students are tasked with graphing the function and identifying its vertical asymptote.	Rational Functions and Equations
Math Example--Rational Concepts--Graphs of Rational Functions: Example 12	Math Example--Rational Concepts--Graphs of Rational Functions: Example 12 Topic Rational Functions Description This example illustrates the graph of the rational function y = (x + 1) / ((x + 2)(x + 4)). The graph features two vertical asymptotes at x = -2 and x = -4, and displays three distinct branches, with one in each of the first, second, and third quadrants. 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 13	Math Example--Rational Concepts--Graphs of Rational Functions: Example 13 Topic Rational Functions Description This example presents the graph of the rational function y = (x - 3) / ((x + 3)(x + 5)). The graph features vertical asymptotes at x = -3 and x = -5, illustrating how the function behaves near these 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 14	Math Example--Rational Concepts--Graphs of Rational Functions: Example 14 Topic Rational Functions Description This example illustrates the graph of the rational function y = (x + 3) / ((x - 1)(x + 4)). The graph features vertical asymptotes at x = -4 and x = 1, displaying how the function behaves near these 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 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