Illustrative Mathematics
Using Function Notation I
Show learners that function notation and multiplication notation are not the same. In the example, Katie is given a function, C(x), which is the cost of producing x amount of DVDs. Ask learners if Katie can divide the function notation,...
Illustrative Mathematics
Points on a Graph
Learners practice using their knowledge of how to interpret a function and use function notation. The activity includes two questions. Given an input of a function and its output, the first question asks learners to write the ordered...
Willow Tree
Functions
What makes a function a function? Learn the criteria for a relation defined as a function both numerically and graphically. Once young mathematicians define a function, they use function notation to evaluate it.
Flipped Math
Functions, Domain and Range
Take a deeper dive into the notation of a function. The video presentation uses grocery store prices as an example to explain the concept of a function. Pupils determine whether mappings are functions or not and find the domain and...
West Contra Costa Unified School District
Evaluating Functions
Functions as inputs for other functions? After reviewing function notation and how to input values to evaluate functions, class members input functions into functions, essentially determining the composition of functions.
EngageNY
Inverse Trigonometric Functions
Build on the understanding of finding angles using trigonometric ratios. Pupils develop the definitions of inverse trigonometric functions by restricting their domains in the 13th instructional activity of a 16-part series. They use...
Modesto Junior College
Graphical Transformations of Functions
Transform your knowledge from average to excellent with this comprehensive guide to function transformations. All of the types of shifts, stretches, and reflections are included with an explanation and coordinating graph to show...
Curated OER
Using Function Notation II
Learners write an example to show a function statement true and another to show it false in this short task that addresses some common student misconceptions.
Virginia Department of Education
Functions 1
Scholars learn what it means for a relation to be a function and see various representations of functions. After learning the definition, they participate in a card sorting activity classifying relations as functions or not.
EngageNY
Formal Definition of a Function
Formalize the notion of a function. Scholars continue their exploration of functions in the second lesson of the module. They consider functions as input-output machines and develop function rules for selected functions.
EngageNY
Function Composition
Combine functions for the first time. Pupils investigate composition of functions using a function table and then function machines in the 17th installment in a 23-part Precalculus series. Scholars learn the two notations for composition...
Flipped Math
Exponential Growth
They grow by leaps and bounds. Learners watch a quick review on function notation as they prepare to learn more about exponential growth. Using their knowledge from sequences, pupils find out whether a function is linear or exponential,...
EngageNY
Solving Problems by Function Composition
Stay composed while solving problems. Learners put their knowledge of compositions to solve problems. To connect with the concept, scholars compose equations to answer questions from real-world situations. Finally, pupils practice using...
Curated OER
Intersecting Graphs
Ninth graders know how to solve a system of linear equations, but what happens when the system involves an exponential function? The instructional slideshow teaches viewers to determine solutions to systems of equations with linear and...
Rice University
Precalculus
Take a step beyond Algebra 2. Learners use the eBook to learn concepts from the typical Precalculus course. Content starts off with a short review of functions in general and moves on to the basic functions, finishing up with more...
West Contra Costa Unified School District
Average Rate of Change
The concept of slope gets an approachable, yet theoretical, treatment in a comprehensive algebra lesson. The use of functional notation and problem-solving techniques keep the material rigorous, but detailed teaching notes and lots of...
Shoreline Community College
Properties of Logarithmic Functions
Use a straightforward approach to understanding logarithmic properties and their role in solving exponential and logarithmic equations to your math class. The lesson begins with an overview of a logarithmic function and its connection to...
Flipped Math
Calculus AB/BC - Defining the Derivative of a Function and Using Derivative Notation
Pupils learn how to find the derivative of a function by applying the definition using limits. Learners understand that the derivative provides the slope of the tangent line and use that information to find the equation of the tangent...
Mathematics Vision Project
Module 1: Sequences
Take steps into sequences. An 11-lesson unit builds upon pupils' previous understanding of writing expressions to develop the idea of sequences. The resource explores both arithmetic and geometric sequences using recursive and explicit...
Willow Tree
Arithmetic and Geometric Sequences
Old mathematicians never die; they just lose some of their functions. Studying sequences gives scholars an opportunity to use a new notation. Learners write functions to model arithmetic and geometric sequences and use them to find new...
Flipped Math
Calculus AB/BC - Defining Limits and Using Limit Notation
There's no limit to what one can learn about limits. The second of 18 videos in Unit 1 - Limits and Continuity focuses on understanding the basic concept of a limit. Pupils learn the definition of limits and see how to determine a limit...
Flipped Math
Calculus AB/BC - Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
Calculus classes definitely need to learn about indefinite integrals. Individuals watch an informative video to learn the antiderivative rules for exponential, logarithmic, trigonometric, and inverse trigonometric functions. To solidify...
Flipped Math
Sequences
Develop a sequence of descriptions. Learners watch an introduction to sequences, their notations, and how to graph them. Pupils use full sentences to describe the sequence and how to get from one term to the next, without needing to...
Curated OER
Study Guide for the Advanced Placement Calculus AB Examination
Is this going to be on the test? A calculus study guide provides an organized list of important topics and a few examples with answers. The topics include elementary functions, limits, differential calculus, and integral calculus,...
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