Shodor Education Foundation
Derivate
Derive tangent lines through derivatives. Scholars use an app to graph functions and investigate derivatives and tangent lines. The interactive automatically graphs a tangent line at a specified point and can also produce tables of values.
CK-12 Foundation
Derivatives with Mean Value Theorem and Rolle's Theorem: Maxima and Minima
Rolle with the mean values and derivatives. Scholars complete the statements of Rolle's Theorem and the Mean Value Theorem. Using the interactive to illustrate scenarios, pupils respond to questions concerning the theorems in terms of...
Curated OER
Worksheet 26 - Functions & Logarithms
In this function and logarithms worksheet, students find the domain and range of functions, use the properties of logs to solve equations. This one-page worksheet contains nine multi-step problems.
West Contra Costa Unified School District
Derivative Theorems
Put all of the derivative rules into one basket. The lesson stars with warm-up exercises that provide a connection to previously learned concepts. The lesson plan uses the different derivative theorems to calculate a variety 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
Derivatives of Inverse Functions
For this derivatives worksheet, students use the chain rule to show equalities between functions. They read a tutorial that guides them through the process of using the chain rule to find derivatives. This worksheet includes five short...
EngageNY
Graphs of Simple Nonlinear Functions
Time to move on to nonlinear functions. Scholars create input/output tables and use these to graph simple nonlinear functions. They calculate rates of change to distinguish between linear and nonlinear functions.
EngageNY
Piecewise Functions
Show your class members that if they can graph a linear function, they can graph an absolute value function. Groups create an absolute value graph using a table, then entertain the idea of an absolute value function defined as two pieces...
EngageNY
Graphs of Exponential Functions and Logarithmic Functions
Graphing by hand does have its advantages. The 19th installment of a 35-part module prompts pupils to use skills from previous lessons to graph exponential and logarithmic functions. They reflect each function type over a diagonal line...
EngageNY
The Inverse Relationship Between Logarithmic and Exponential Functions
Introducing inverse functions! The 20th installment of a 35-part lesson encourages scholars to learn the definition of inverse functions and how to find them. The lesson considers all types of functions, not just exponential and...
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 lesson of a 16-part series. They use inverse functional...
EngageNY
Graphing the Tangent Function
Help learners discover the unique characteristics of the tangent function. Working in teams, pupils create tables of values for different intervals of the tangent function. Through teamwork, they discover the periodicity, frequency, and...
EngageNY
The “WhatPower” Function
The Function That Shall Not Be Named? The eighth installment of a 35-part module uses a WhatPower function to introduce scholars to the concept of a logarithmic function without actually naming the function. Once pupils are comfortable...
EngageNY
Translating Graphs of Functions
If you know one, you know them all! Parent functions all handle translations the same. This lesson examines the quadratic, absolute value, and square root functions. Pupils discover the similarities in the behavior of the graphs when...
EngageNY
Stretching and Shrinking Graphs of Functions
Why is that graph wider? Pupils learn about stretching and shrinking graphs of square root, absolute value, cubic, and quadratic functions. They study both vertical and horizontal stretches and shrinks in addition to reflections.
EngageNY
Revisiting the Graphs of the Trigonometric Functions
Use the graphs of the trigonometric functions to set the stage to inverse functions. The lesson reviews the graphs of the basic trigonometric functions and their transformations. Pupils use their knowledge of graphing functions to model...
EngageNY
Formal Definition of a Function
Formalize the notion of a function. Scholars continue their exploration of functions in the second lesson plan of the module. They consider functions as input-output machines and develop function rules for selected functions.
EngageNY
Linear Functions and Proportionality
Connect linear equations, proportionality, and constant rates of change to linear functions. Young mathematicians learn how linear equations of the form y = mx + b can represent linear functions. They then explore examples of linear...
EngageNY
Transforming the Graph of the Sine Function
Build a solid understanding of trigonometric transformations through exploration. Learners work in teams to analyze the effects of different algebraic components on the graph of a sine function.
EngageNY
Piecewise and Step Functions in Context
Looking for an application for step functions? This activity uses real data to examine piecewise step functions. Groups create a list of data from varying scenarios and create a model to use to make recommendations to increase revenue.
EngageNY
Modeling with Inverse Trigonometric Functions 2
Use inverse trigonometric functions to work with ramps, rabbits, and Talladega. The class models real-world situations with trigonometric functions and solves them using inverses in the 15th installment of a 16-part series. Pupils solve...
EngageNY
Graphs of Functions and Equations
Explore the graphs of functions and equations with a resource that teaches scholars how to graph functions as a set of input-output points. They learn how the graph of a function is the graph of its associated equation.
EngageNY
Structure in Graphs of Polynomial Functions
Don't allow those polynomial functions to misbehave! Understand the end behavior of a polynomial function based on the degree and leading coefficient. Learners examine the patterns of even and odd degree polynomials and apply them to...
EngageNY
Graphs of Piecewise Linear Functions
Everybody loves video day! Grab your class's attention with this well-designed and engaging resource about graphing. The video introduces a scenario that will be graphed with a piecewise function, then makes a connection to domain...