Illustrative Mathematics
Building an Explicit Quadratic Function by Composition
Use equivalent expressions to reveal information about their graphs. Pupils verify that two quadratic functions are equivalent. By comparing the two expressions, they determine the vertex, the zeros, the y-intercept, and the direction it...
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Composition Of Functions
Students investigate the concept of a function and practice using the notation and compute the values of composite functions. They use the examples provided in the lesson for guided practice with scaffolding provided by the teacher.
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Worksheet 12: Functions
In this math worksheet, students are given 7 problems in which they differentiate, figure rate of change, determine value, and prove formulas.
Illustrative Mathematics
Temperature Conversions
Complete two conversions at once using compositions. Pupils use the conversion formulas for temperatures to calculate a formula to convert directly between Kelvin and Fahrenheit. Classmates determine the meanings of composition notation...
Concord Consortium
Gravity
Weight is a function of the distance from sea level. Learners explore the many implications of this fact in an inquiry-based task. Given the function, pupils answer questions before manipulating the function to rewrite the distance from...
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Function Composition
Students solve two functions at once. In this algebra lesson, students add, subtract, multiply and divide composition functions. They use the correct notation and substitution to get their answer.
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Operations with Functions Including Composition
Students explain functions. In this function lesson, students solve functions. Groups of students develop strategies to perform operations with functions. They write test questions using functions which include all operations...
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Operations on Functions
In this operations and functions worksheet, students add, subtract, multiply, and divide functions. This one-page worksheet contains 18 multi-step problems.
University of North Texas
Math Exam 1 Review
Perfect as a review guide, this instructional activity provides a range of questions focusing on functions. Topics include composing functions, transformations, domains, and polynomials. Also included are corresponding worksheets...
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Worksheet 7.4 Function Composition
In this function composition worksheet, students find the composition of functions and state the domain. They graph relations and state the inverse. This two-page worksheet contains twelve multi-step problems.
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Limits of Composition Functions
In this limits worksheet, students find the limits of 9 composition functions. Students evaluate limits for each function at a specific value or as it approaches any value.
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Related Functions
In this function worksheet, students discuss how a function would change if it shifted on a graph. They create ten new, related functions. Students identify odd, even and symmetric functions. This two-page worksheet contains examples,...
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Composition of Functions and the Chain Rule
In this function worksheet, students determine the natural domain and range for functions and formulas. They identify the composition of two functions and complete the derivation of the quotient rule. This three-page worksheet contains...
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Your Father
Your learners will explore the idea that not all functions have real numbers as domain and range values as seen in this real-life context. Secondly, the characteristics required for a function to have an inverse are explored including...
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Exploring Transformations
Students explore what happens when geometric figures are transformed on the coordinate plane. They work in pairs, moving geometric shapes in the plane, and formalize their rules as functions.
Illustrative Mathematics
Building an Explicit Quadratic Function by Composition
Use an activity to illustrate the different forms of a quadratic function. Here, the task asks learners to use composition of given functions to build an explicit function. The process emphasizes the impact of the order of composition...
EngageNY
End-of-Module 3 Assessment Task
Let'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...
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Composite Functions
Young scholars create a poster to explain composite functions. In this composite function worksheet, students explore linear equations and functions. They complete a worksheet and use manipulatives to complete problems.
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Complex Analysis: Complex Function
In this complex function worksheet students identify the derivative of given functions and explore the rules of differentiation. This two-page worksheet contains explanations and examples, followed by ten problems.
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The Functional Notation Problem
In this composite functions instructional activity, students solve 1 composite functions problem by finding f(2x) in terms of f(x). Students use a rational function when finding f(2x).
EngageNY
Restricting the Domain
But what if the function cannot be inverted? Pupils continue to work with inverses of functions using tables, graphs, and algebraic equations. They restrict the domain of non-invertible functions to make them invertible. Using...
Illustrative Mathematics
Flu on Campus
An outbreak of the swine flu on a school campus has caused an increase in the number of boxes of tissues sold by the school store. In a real-world-modeling activity, pupils use composition of functions to determine how the number of...
CK-12 Foundation
Chain Rule
Keep it on the chains. Pupils work through the steps in the chain rule using the interactive as a guide. Learners identify the two composed functions and their associated derivatives from a set of choices. They continue on to build the...
Curated OER
Graphs of Functions
In this function activity, learners sketch graphs of functions, write functions as a composition of two or three functions, and differentiate functions. This three-page activity contains approximately 33 problems.