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Continuous Function Teacher Resources
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For this multivariable function worksheet, students find the limits of a function, identify the domain, and explore continuous functions. This two page worksheet contains explanations, definitions, and examples. There are approximately four multi-step problems in this worksheet.
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.
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.
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.
In this math worksheet students use the intermediate value theorem to solve two problems. They find parallel lines that will cut a convex shape into two pieces with equal areas. Students repeat this problem with a concave shape. Students show that there are always two points on exact opposite sides of earth that have the same temperature. Students use the mean-value theorem to find the derivative of a function.