Continuous Functions Teacher Resources
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In this continuous function worksheet, learners examine a graph. They determine a rate during an interval of time. This one-page worksheet contains five multi-step problems.
Mean Value Theorem
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 slope of the function over that interval. Here, Sal also uses and informally defines the terms: continuous function, differential, and closed and open interval.
Graphical Consequences of Continuity
Students explore and examine the continuity of three functions: horizontal zooming, polynomial function, and oscillating functions. They practice graphing functions, generating tables and navigating the zoom, vars and test menus on their graphing hand held calculators.
Worksheet 6: Functions
In this math worksheet, students answer 7 questions having to do with continuous functions, the Squeeze Theorem, and the Product Rule for differentiation.
Multivariable Calculus: Limits of Multivariable Functions
In this multivariable function learning exercise, students find the limits of a function, identify the domain, and explore continuous functions. This two page learning exercise contains explanations, definitions, and examples. There are approximately four multi-step problems in this learning exercise.
Clarification and Extra Problems for Homework 10: Metric Space
For this metric space worksheet, students define a compact metric space, and explore continuous functions. They prove a function converges uniformly. This one-page worksheet contains six problems.
Worksheet 10: Continuous Functions
In this math worksheet, students answer 7 questions regarding continuous functions, domains, differentiables, and inverse functions.
In this continuous function learning exercise, students identify continuous functions, and use limits to determine the horizontal asymptotes. This two-page learning exercise contains three problems.
In this continuous function activity, students determine the average velocity of objects over given intervals of time. They compute the derivative of functions and determine the slope of a line. This four-page activity contains approximately 25 multi-step problems.
Choosing a Cell Phone Plan
Here is an activity that should catch the attention of your class! It focuses on the real-world problem of selecting the best cellular phone plan. This exercise would be especially good to use when introducing piecewise functions. Learners compare costs for various data plans, considering such features as unlimited talk and unlimited texts, to determine which plan is the most cost effective for different scenarios. The task requires giving graphical and numerical representations of the options and writing a justification for choosing a particular plan. The resource includes a detailed commentary for the teacher and three follow-up questions.
Limit Examples w/ brain malfunction on first prob (part 4)
Sal explores more complex limit problems including showing how to take the limit of an expression with a square root by using the conjugate and how to simplify trigonometric functions that are part of limit problems. Note: A mistake is made on the last step of first problem where multiplication should have been used instead of addition, resulting in the correct answer of 3/16.
Learners investigate the intervals represented by a function in this calculus lesson. They decide what interval of the function will be positive, negative or zero. They are then given graphs of functions and asked to analyze it.
Neurons and the Nervous System
The highlight of this series is activitiy #4. Anatomy pupils examine slides of three unknown cells. With the function of the nervous system in mind, they consider the structure of each and try to guess which one is part of that system. In other activities, they examine the nervous system of earthworm and grasshopper specimens, or they study drawings of different animal nervous systems. The drawings unfortunately aren't included in this resource; however, they can be accessed through the National Science Teachers Association website.
The Unit Circle
Students solve problems using the unit circle. In this precalculus lesson, students identify angles using the properties of the unit circle. They observe the trigonometric graphs and sine, cosine and tangent.
Life Systems- Interacting Organisms
Participate in a life science unit that examines the relationships of living organisms to each other and to their environment as well as the student's role in the cycle of life. Through hands-on activities, research, and scientific investigations they explore the problem of persistent pollutants and their harmful effects on both humans and ecosystems.
Linear Functions: Are You Ready for the Real World?
Here's a real-world lesson using a business simulation. Two business accounts are used to find slope and intercept functions. The class graphs and interprets the information to find a break even point. There are plenty of worksheets and assessments included in this lesson.
Classifying Functions-Grade 11
Investigate non-linear functions based upon the characteristics of the function or the representation of the function. The functions are displayed in multiple formats including as graphs, symbols, words, and tables. Learners use written reflection scored on a rubric to assess understanding.
Drip, Drop, Drip, Drop
Design an experiment to model a leaky faucet and determine the amount of water wasted due to the leak. Middle schoolers graph and write an equation for a line of best fit. They use their derived equation to make predictions about the amount of water that whould be wasted from one leak over a long period of time or the amount wasted by serveral leaks during a specific time period.
Students investigate limits and continuity of functions. In this limits and continuity of functions instructional activity, students find the limit as a function approaches a given value. Students find the domain of functions.
Modeling Natural Disaster with Mathematical Functions
Ninth graders investigate the functional relationship of different environmental phenomena. In this math lesson, 9th graders create models of various natural disasters. They use logarithmic and exponential functions to interpret population growth.