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Assessment
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\n\"Sorting\n\n
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\nInside Mathematics\n
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\nSorting Functions\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nGraph A goes with equation C, but table B. The short assessment task requires class members to match graphs with their corresponding tables, equations, and verbalized rules. Pupils then provide explanations on the process they used to...\n
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Interactive
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\n\"Analyzing\n\n
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\nCK-12 Foundation\n
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\nAnalyzing the Graphs of Functions: Analyzing a Rational Function\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nShift the function and transform the key features of the graph. By translating the graph of the rational function, class members find out how the key features alter. Pupils determine the domain, range, asymptotes, and intervals of...\n
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Assessment
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\n\"Test\n\n
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\nMt. San Antonio Collage\n
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\nTest 1: Graphing Functions\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nGraph the night away with all the different types of functions provided in the worksheet. Linear, quadratic, and rational all ask for graphs, domain and range and other key factors about the functions.\n
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Lesson Plan
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\n\"Driving\n\n
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\nK20 LEARN\n
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\nDriving Rationally: Introduction To Rational Functions And Asymptotes\n

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\n\nFor Teachers\n\n11th\n\nStandards\n
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\nCalculating average speeds is not as simple as finding an average. The lesson introduces class members to rational functions by presenting a problem about finding an average speed for the rest of a trip. Pupils develop an equation to...\n
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Assessment
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\n\"Graphs\n\n
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\nInside Mathematics\n
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\nGraphs (2004)\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nShow your pupils that perimeter is linear and area is quadratic in nature with a short assessment task that requests learners to connect the graph and equation to a description about perimeter or area. Scholars then provide a...\n
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Activity
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\n\"Students\n\n
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\nPBL Pathways\n
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\nStudents and Teachers 2\n

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\n\nFor Students\n\n10th - Higher Ed\n\nStandards\n
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\nExamine trends in student-to-teacher ratios over time. Building from the first task in the two-part series, classes now explore the pattern of student-to-teacher ratios using a non-linear function. After trying to connect the pattern to...\n
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Assessment
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\n\"Sorting\n\n
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\nMathematics Assessment Project\n
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\nSorting Functions\n

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\n\nFor Students\n\n9th - 11th\n\nStandards\n
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\nThere's no sorting hat here. A high school assessment task prompts learners to analyze different types of functions. They investigate graphs, equations, tables, and verbal rules for four different functions.\n
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Assessment
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\n\"Getting\n\n
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\nBalanced Assessment\n
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\nGetting Closer\n

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\n\nFor Students\n\n11th - 12th\n\nStandards\n
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\nFlip the script! Reverse the situation and ask the class to find the function given asymptotes. The task requires class members to use their knowledge of functions and asymptotes to create functions that have a given asymptote or...\n
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Interactive
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\n\"Horizontal\n\n
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\nCK-12 Foundation\n
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\nHorizontal and Vertical Asymptotes: Rational Functions\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nPlay with the graph of a rational function to discover the asymptote patterns. Young scholars use the interactive lesson to discover the relationship between the asymptotes and the function. As they manipulate the function, the graph...\n
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Activity
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\n\"Doctors\n\n
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\nPBL Pathways\n
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\nDoctors and Nurses\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nHow many nurses does it take to support one doctor? A project-based activity asks learners to analyze state data to answer this question. Classes create polynomial functions from the data of doctors and nurses over a seven-year...\n
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Instructional Video3:25
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\n\"Reciprocal\n\n
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\nFuseSchool\n
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\nReciprocal Graphs\n

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\nExplore the patterns of a reciprocal function with an engaging video lesson that compares graphs of reciprocal functions to different polynomial functions. After describing the key features, the instructor explains the patterns that...\n
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Activity
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\n\"Cell\n\n
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\nPBL Pathways\n
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\nCell Phones\n

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\n\nFor Teachers\n\n10th - Higher Ed\n\nStandards\n
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\nCalling all subscribers! Model revenue based on individual cell phone subscribers. The project-based learning activity presents a challenge to scholars from a cell phone company. Individuals model data provided to them from the company...\n
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Interactive
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\n\"Oblique\n\n
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\nCK-12 Foundation\n
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\nOblique Asymptotes: Rational Functions and Asymptotes\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nExamine the connection between rational functions and their graphs. Individuals use an online manipulative to sort equations with horizontal and oblique asymptotes. They focus on the degree of the numerator and denominator.\n
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Assessment
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\n\"End-of-Module\n\n
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\nEngageNY\n
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\nEnd-of-Module 3 Assessment Task\n

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\n\nFor Teachers\n\n11th - 12th\n\nStandards\n
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\nLet's see what the class learned! The last installment of the 23-part Pre-calculus module consists of nine assessment questions designed to measure a specific portion of a standard in the unit. Learners demonstrate their understanding of...\n
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Interactive
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\n\"Desmos\n\n
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\nDesmos\n
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\nDesmos Graphing Calculator\n

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\n\nFor Students\n\n9th - Higher Ed\n\nStandards\n
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\nThey say a graph is worth a thousand points. The interactive allows users to graph a wide variety of functions and equations. Using the included keyboard or typing directly into the list, learners determine the graph of a function....\n
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Instructional Video11:21
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\n\"Equations\n\n
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\nCorbett Maths\n
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\nEquations Involving Algebraic Fractions (Advanced)\n

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\n\nFor Students\n\n9th - 11th\n\nStandards\n
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\nEveryone seems to freeze when they see a fraction! Give your classes a lesson to watch and rewatch until they are comfortable with the process of solving rational equations. A video presenter demonstrates solving two rational equations....\n
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Lesson Plan
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\n\"Asymptotes\n\n
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\nCurated OER\n
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\nAsymptotes and Zeros\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nLearn how to explore rational functions and investigate the graphs rational functions and identify its singularities and asymptotes.  Students approximate the solutions to rational equations and inequalities by graphing.\n
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Worksheet
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\n\"Graphing\n\n
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\nCurated OER\n
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\nGraphing a Rational Function\n

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\n\nFor Students\n\n10th - 12th\n
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\nIn this graphing rational functions worksheet, students find the domain, asymptotes, intercepts and graph a given rational function.  A grid for the graph is provided.\n
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Lesson Plan
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\n\"Comparing\n\n
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\nEngageNY\n
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\nComparing Rational Expressions\n

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\n\nFor Students\n\n10th - 12th\n\nStandards\n
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\nIntroduce a new type of function through discovery. Math learners build an understanding of rational expressions by creating tables and graphing the result. \n
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Lesson Plan
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\n\"Direct,\n\n
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\nCurated OER\n
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\nDirect, Inverse and Joint Variation\n

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\n\nFor Teachers\n\n11th\n
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\nEleventh graders identify, create and solve word problems involving inverse variation. In this algebra lesson, 11th graders solve problems using direct, inverse and joint variation. They identify problems using these methods.\n
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Website
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\n\"Binghamton\n\n
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\nOther\n
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\nBinghamton University: Graphing Rational Functions [Pdf]\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nThis site is a 16-page excerpt from a textbook that discusses the topic of graphing rational functions. The book includes numerous worked out examples. Topics that are covered include the domain of a rational function, zeroes of a...\n
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Activity
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\n\"Coolmath:\n\n
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\nCool Math\n
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\nCoolmath: Graphing Rational Functions Putting It All Together\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nA tutorial reviewing graphing rational functions.\n
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Activity
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\n\"Coolmath:\n\n
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\nCool Math\n
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\nCoolmath: Graphing Rational Functions X and Y Intercepts\n

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\n\nFor Students\n\n6th - 8th\n\nStandards\n
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\nFind out how to find the x and y-intercepts when graphing rational functions.\n
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Activity
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\n\"Coolmath:\n\n
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\nCool Math\n
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\nCoolmath: Graphing Rational Functions Vertical Asymptotes\n

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\n\nFor Students\n\n6th - 8th\n
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\nThis Precalculus review (Calculus preview) lesson explains how to find the vertical asymptotes when graphing rational functions.\n
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\n\nGet Free Access\n\nSee Review\n
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