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Horizontal and Vertical Asymptotes of Graphs of Rational Functions
Get close to your favorite line. Scholars use end behavior to help find horizontal asymptotes. With the understanding of domains of rational functions, learners find vertical asymptotes and then use graphing calculators to verify the...
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Transformation of Graphs
In this college level Pre-calculus worksheet, students examine families of functions and describe how graphs of the transformation can be obtained from the parent graph. The four page worksheet contains seventy-two problems. Answers...
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Introduction to Limits
High schoolers practice using graphing calculators and spreadsheets as they explore numeric limits using sequences and functions. They complete a sequencing worksheet, and determine which sequence corresponds to story a story called...
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Functional Analysis
Students perform functional analysis. For this pre-calculus lesson, students recognize the different elements of a function, graph a function and analyze it. They synthesize composites of other basic functions.
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Graphs and Data
Students investigate poverty using graphs. In this algebra lesson plan, students collect data on the effects of poverty and use different rules to analyze the data. They graph and use the trapezoid rule to interpret the data.
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Function and Graphs
In this college level Pre-Calculus worksheet, students determine if a given relation is a function, graph functions and observe their behavior, and determine if a function is even, odd, both, or neither. The four page worksheet contains...
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Exponential Equations and Functions
For this college level Pre-Calculus worksheet, students solve problems involving exponential functions. Students determine the domain, range, y-intercept and asymptotes of exponential functions. The three page worksheet contains seventy...
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Graphs of the Sine and Cosine Function
In this college level Pre-Calculus worksheet, students investigate the graphs of the sine and cosine functions. The six page worksheet contains seventy-eight problems. Solutions are not provided.
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Mathematices: Pre-Calculus
Young scholars relate polynomials to real life situations. In this algebra instructional activity, students graph equations through modeling and data collection. They must be comfortable doing word problems.
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Vertical and Horizontal Translations
Pupils analyze function graphs. In this Algebra II/Pre-calculus lesson, students investigate the graph of a function as they determine to which family of functions it belongs, determine the parent function and describe the translation...
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Lesson #45 Graphs of Logarithmic and Exponential Functions
Students investigate exponential and logarithmic functions. In this Pre-calculus/Calculus instructional activity, students investigate the relationship between y = ln(x) and y = e^x. Students graph the functions and show they are...
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Linear and Quadratic Approximations
Students explore a linear, a parabolic, and a log function. In this Algebra II/Pre-calculus lesson students investigate the graph a line, a parabola, and a log function. Students examine the three graphs as they compare and contrast...
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Properties of Logarithms
Learners explore the concept of logarithms. In this logarithms activity, students discuss the logarithm properties. Learners use linear functions as a basis to develop the logarithm properites by substituting log b and log a for x and y.
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Computer Graphing Calculator Explorations
High schoolers explore the graphing calculator feature on the Macintosh computer to explore some "parent" functions and their translations, combinations, and composites.
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Graph of the Tangent, cotangent, Secant, and Cosecant Functions
In this college level Pre-calculus worksheet, students examine the graphs of the Tangent, cotangent, secant, and cosecant functions. Students find the intercepts and any asymptotes. The seven page worksheet contains sixty-six...
National Security Agency
Multiple Representations of Limits
After an introductory activity to demonstrate the theory of a limit, additional activities approach a limit from graphical, numerical, and algebraic methods. The activity looks at the multiple ways of understanding and evaluating a limit.
West Contra Costa Unified School District
Introduction to Logarithms
Build on pupils' understanding of inverse functions by connecting logarithmic functions to exponential functions. This activity allows individuals to see graphically the inverse relationship between an exponential and logarithmic...
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Graph Of The Derivative
Students engage in a lesson that is concerned with defining and drawing the graph of a derivative. The lesson includes a definition and examples to lead them away from any misconceptions. They graph derivatives using examples that are...
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Precalculus: Function Models for Real-Life Situations
Young scholars use calculators and "by hand" techniques to compare models of real-life data situations, determine the best model for a situation, and use their models to make predictions.
Shodor Education Foundation
InteGreat
Hands-on investigation of Riemann sums becomes possible without intensive arithmetic gymnastics with this interactive lesson plan. Learners manipulate online graphing tools to develop and test theories about right, left, and midpoint...
West Contra Costa Unified School District
Interest and the Number e
Mary, Mary, quite continuously, how does your money grow? Uses examples to examine the difference between simple interest and compound interest, and to take a look at different rates of compounding. Learners explore what would happen as...
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Is there Treasure in Trash?
More people, more garbage! Young environmentalists graph population growth against the amount of garbage generated per year and find a linear model that best fits the data. This is an older resource that could benefit from more recent...
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Extrema on an Interval
Young scholars explore maximum and minimum points, slopes and tangents. In this Pre-Calculus instructional activity, students solve optimization problems and find rates of change.
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Decode Word Is..
Students solve problems using patterns. In this algebra lesson, students identify the relation, domain and range of a function. They graph functions using coordinate pairs.