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Intuitive Approach to Limits
Students identify and comprehend the concept of limit in mathematics. They also view artistic works illustrating limits by M. C. Escher and apply techniques of one-sided limits to graphs of relations. Finally, students compute limits...
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Graphing Rational Functions
Learners complete an activity, included, of the information on asymptotes and intercepts. They also solve and complete eight questions on graphing rational functions, file included. Finally, pupils summarize vertical asymptotes,...
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Rational Functions and Conics
In this math worksheet, students practice the calculation of rational functions and conics. This worksheet has 6 problems for the students to solve.
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Horizontal Asymptotes: M=N, M>N
In this algebra worksheet, students calculate the horizontal asymptote for rational functions, whose leading exponents follow the rules: M = N or M > N. There are 4 questions.
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Worksheet 5 Math 126-Hyperbolas
In this Pre-calculus learning exercise, students solve problems involving hyperbolas. The two page learning exercise contains explanation and four multi-part questions. Answers are not included.
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Rational Expressions Test with a Calculator
In this rational expression worksheet, students graph rational equations, evaluate limits, state intercepts, asymptotes, and roots and factor. This worksheet is designed as a test to be completed with a calculator.
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Rational Functions and Their Graphs
In this Algebra II instructional activity, 11th graders examine the graphs of rational functions, identifying the points of discontinuity and the vertical and horizontal asymptotes. The three page instructional activity contains...
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Crossing the Asymptote
Students investigate graphs and their asymptotes. In this precalculus lesson, students examine the numerator and denominator of their rational functions. This helps them identify where and when the graph will cross its asymptote.
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Twenty Rational Function Problems
In this rational functions worksheet, students find asymptotes, perform operations, simplify, and solve in twenty rational functions.
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Properties of Curves
In this Calculus worksheet, students use a graphing calculator to boost their understanding of functions and their graphs as they examine the properties of curves. The forty-two page worksheet contains one hundred problems. Answers are...
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A Slant Asymptote
In this slant asymptote worksheet, learners solve 1 rational equation. Students determine the slant asymptote of a rational equation.
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Graphing Review
in this graphing review worksheet, students solve a variety of problems such as interpreting parabolas, identifying intercepts and asymptotes, and identifying functions. They solve piecewise functions and rational functions. This twenty...
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Reciprocals of Quadratic Functions
Eleventh graders investigate inverse functions. In this Algebra II lesson, 11th graders use their prior knowledge of linear, exponential,and quadratic functions to create a graph of an equation they have never seen before.
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Simplifying Functions
In this simplifying functions learning exercise, 11th graders solve and complete 11 different types of problems. First, they simplify each function as necessary. Then, students state the vertical asymptotes, holes, horizontal asymptotes,...
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Intervals
In this intervals worksheet, students solve and complete 8 various types of problems. First, they find the intervals of x for each curve. Then, students sketch a graph of each showing all maximum and minimum points and all inflection...
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Graphing Functions
In this graphing functions activity, students solve and complete 16 various types of problems. First, they evaluate each of the limits provided. Then, students graph each of the functions and their asymptotes as given.
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Inflection Points
In this inflection points worksheet, 11th graders solve and complete 5 different problems. First, they find intervals of x for which each of the following curves is increasing, decreasing, concave upward, concave downward. Then, students...
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Chapter 3: Practice Test - Functions
In this function activity, students find the inverse of functions, determine the horizontal asymptote of functions and graph functions. This three-page activity contains 27 problems.
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The Reciprocal Function Family
In this Algebra II worksheet, 11th graders examine the reciprocal function family in the form y = a/(x – h) + k, identifying the vertical and horizontal asymptotes. The two page worksheet contains explanation, examples, and two practice...
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Hyperbolas
Students locate and identify the center, foci, vertices, and asymptotes fo hyperbolas. They graph equations involving asymptotes and hyperbolas. Finally, students determine the equation of a hyperbola with a horizontal transverse axis.