CK-12 Foundation
Intermediate Value Theorem, Existence of Solutions: Function Exploration
Does the value exist? The interactive allows pupils to visualize the Intermediate Value Theorem. Using the visualization, individuals respond to questions using specific values and general values. The class comes to the conclusion what...
CK-12 Foundation
Continuity at a Point, Continuity Test, Types of Discontinuity: Properties of Continuous Functions
Take a closer look at continuous functions within given intervals. Using the parent cubic function, learners explore properties of continuous functions on intervals. Pupils interpret the Intermediate Value Theorem and the Extreme Value...
Mathematics Vision Project
Features of Functions
What are some basic features of functions? By looking at functions in graphs, tables, and equations, pupils compare them and find similarities and differences in general features. They use attributes such as intervals of...
Mathematics Vision Project
Linear and Exponential Functions
Provide a continuous progression to linear and exponential functions. Pupils continue to work with the discrete functions known as sequences to the broader linear and exponential functions. The second unit in a series of nine provides...
PBL Pathways
Medical Insurance 3
Create a technical report explaining the components of a medical plan through a function. The project-based learning activity gives a medical insurance scenario that young mathematicians model using piecewise functions. Their analyses...
Illustrative Mathematics
Invertible or Not?
Two for one—create an invertible and non-invertible function from the same data. The task presents a function table with missing outputs for the class to use to create two functions. One of the functions should have an inverse while the...
Balanced Assessment
Melons and Melon Juice
Model the difference between the graphs of discrete and continuous functions. Scholars examine two scenarios and construct graphs to model the situation. They then compare their graphs that illustrate the subtle difference between these...
EngageNY
More Examples of Functions
Discrete or not discrete? Individuals learn about the difference between discrete and non-discrete functions in the fourth installment of a 12-part module. They classify some examples of functions as being either discrete or non-discrete.
Balanced Assessment
A Sharper Image
Not all continuous functions are differentiable. Pupils find three types of functions that are defined everywhere but not differentiable for all values of x. Along with providing examples of each type of function, students explain the...
University of Northern Texas
Continuity
Continue a study of calculus by using a slideshow to introduce the concept of continuity. After defining the term, the presentation provides examples of functions that are discontinuous and introduces different types of...
Charleston School District
Increasing, Decreasing, Max, and Min
Roller coaster cars traveling along a graph create quite a story! The lesson analyzes both linear and non-linear graphs. Learners determine the intervals that a graph is increasing and/or decreasing and to locate maximum and/or minimum...
Curated OER
Unstable Table
Bothered by a wobbly table? Learn how to fix this problem using concepts of slope and continuity. Pupils first consider the problem in two dimensions and then progress to three dimensions. The solution is really quite simple.
Mathematics Vision Project
Module 5: Features of Functions
The language and features of functions get careful treatment in a complex but doable lesson. Learners get a lot of practice really figuring out what a graph means in context, and also identifying key features of graphs. Key ideas like...
Curated OER
Open Sets, Limits, Continuity
In this open sets worksheet, students give characteristics of an open set under given conditions. They graph functions and define limits. This two-page worksheet contains 3 multi-step problems with explanations.
Curated OER
Piecewise Practice Problems
In this algebra activity, students validate continuity of a graph by a defined interval as well as determine continuity of a piecewise function.
Curated OER
Worksheet 9 - Functions
In this function worksheet, students explain continuous and noncontinuous function and graph derivatives. This two-page worksheet contains seven multi-step problems.
Curated OER
AP Calculus Practice Exam 2008
In this calculus practice exam activity, learners solve 16 multiple choice problems. Students find derivatives, points of continuity, area, rates, etc.
Curated OER
AP Calculus Practice Exam
In this practice exam worksheet, students solve 17 multiple choice problems. Students find derivatives, points of continuity, maximums, minimums, integrals, and area of enclosed regions.
Curated OER
Math 155 - Fall 2002 Worksheet 3: Continuity
For this continuity worksheet, students solve 5 short answer problems about continuity. Students determine where functions are continuous and find the limits of functions at points of discontinuity.
Curated OER
Continuous Probability Distributions
In this continuous probability distribution worksheet, students identify discrete and continuous distributions. They calculate the linear combination of the independent normal random variable and determine probabilities using exponential...
Curated OER
Three Calculus Overview Problems
In this calculus overview activity, students: find the equation of a tangent line, curve sketch, and find limits. Students should have covered continuity as well.
Curated OER
Sixteen Multiple Choice AP Calculus BC Exam Preparation Questions
In this review for Calculus BC exam instructional activity, students solve sixteen various multiple choice problems. These problems are designed as review and preparation for the AP Calculus Exam.
Curated OER
Six Continuity Problems
In this continuity activity, students examine six functions for continuity. Students find values to make a peice-wise function continuous, state domains, use limits, and the Intermediate Value Theorem.
Curated OER
Math 155 - Spring 2002 Worksheet: Limits
In this limits worksheet, students solve 6 short answer problems. Students find the limits of functions, points of discontinuity, and the derivatives of functions.