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79 resources with the concept continuous function

Lesson Planet

Functions Represented by Situations

For Teachers 9th - 12th Standards
What good are functions in the real world? Learners take real-world situations and investigate the associated function. Documentation of real-world scenarios helps learners connect key mathematical vocabulary words with certain functions.
Lesson Planet

Functions Represented by Graphs

For Teachers 9th - 12th Standards
Graph that function! Learners explore how the shape of a graph relates to the function the graph describes. The instructional activity uses teamwork and Function Journals to reinforce new mathematical vocabulary.
3:56
Lesson Planet

Mean Value Theorem

For Students 11th - Higher Ed
Sal spends most this video explaining what the Mean Value Theorem says in a very intuitive way. He follows this with a concrete example of finding the value of a function on a closed interval where the slope is the same as the average...
Lesson Planet

How Much Is Your Time Worth?

For Teachers 9th - 12th Standards
Develop functions with function notation from formulas. With calculators, pupils graph compound interest equations using a given principle amount, rate, and number of times compounded. Learners convert the formula to use function...
Lesson Planet

Absolute Versus Local Extrema

For Students 11th - Higher Ed
Get the class to take an extreme look at functions. The interactive presents a function on a closed interval with a movable tangent line. Using the given function, pupils determine the extrema, critical points, and points of inflection. 
Lesson Planet

Derivatives with Mean Value Theorem and Rolle's Theorem: Maxima and Minima

For Students 11th - Higher Ed
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...
Lesson Planet

Continuity of a Function: Continuity

For Students 10th - Higher Ed
Does the point continually move along the graph? Pupils drag a line across two functions to determine whether they are continuous or not. They answer questions about the properties of continuous and discontinuous functions. Using their...
Lesson Planet

Intermediate Value Theorem, Existence of Solutions: Function Exploration

For Students 11th - Higher Ed
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...
Lesson Planet

Continuity at a Point, Continuity Test, Types of Discontinuity: Properties of Continuous Functions

For Students 11th - Higher Ed
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...
Lesson Planet

Features of Functions

For Teachers 9th - 10th Standards
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...
Lesson Planet

Linear and Exponential Functions

For Teachers 9th - 10th Standards
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...
Lesson Planet

Medical Insurance 3

For Students 11th - Higher Ed Standards
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...
Lesson Planet

Melons and Melon Juice

For Students 9th - 12th Standards
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...
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EngageNY

More Examples of Functions

For Teachers 8th Standards
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.
11:11
Lesson Planet

How to Make a Function Continuous (for a piecewise function)

For Students 11th - Higher Ed
Now do you see how limits relate to continuity? Viewers of this learn to find the value of a constant for a piecewise function that makes it continuous. They see how one-sided limits show that the derived constant is correct.
Lesson Planet

A Sharper Image

For Students 11th - 12th
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...
Lesson Planet

Continuity

For Teachers 11th - Higher Ed
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...
4:36
Lesson Planet

Distinguish Between Discrete and Continuous Graphs

For Students 8th - 11th Standards
Most of us always feel the need to connect the dots together. Wait! Sometimes the graphs are discrete and do not make any sense if they are plotted together. Young adults learn the difference between discrete and continuous graphs, and...
Lesson Planet

Increasing, Decreasing, Max, and Min

For Students 8th Standards
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...
Lesson Planet

Unstable Table

For Teachers 9th - 12th Standards
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.
Lesson Planet

Limits and Continuity

For Teachers 10th - 12th Standards
For learners who are used to smooth lines and curves on graphs, confronting gaps and corners in their functions is often quite disconcerting. These notes, presentation, and worksheet set do an excellent job of breaking down how and when...
Lesson Planet

Finding Limits Using Tables and Graphs

For Teachers 10th - 12th Standards
An excellent set of problems for developing limit intuition in learners, this presentation and homework set leads the class from testing basic continuous functions through to discontinuous piecewise problems. Using both table and...
Lesson Planet

Module 5: Features of Functions

For Teachers 8th - 10th Standards
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...
Lesson Planet

Open Sets, Limits, Continuity

For Students Higher Ed
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.