Continuous Functions Teacher Resources
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In this continuous function learning exercise, students examine a graph. They determine a rate during an interval of time. This one-page learning exercise contains five multi-step problems.
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 answer 7 questions regarding continuous functions, domains, differentiables, and inverse functions.
In this continuous function worksheet, students identify continuous functions, and use limits to determine the horizontal asymptotes. This two-page worksheet contains three problems.
In this continuous function worksheet, 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 worksheet contains approximately 25 multi-step problems.
In this integration instructional activity, students use any method to integrate given problems. They identify a continuous function and determine the area of a triangle inscribed in a square. This one-page instructional activity contains seventeen problems.
In this Intermediate Value Theorem worksheet, students identify and explain a continuous function. They use the Intermediate Value Theorem to prove solutions of equations. This two-page worksheet contains three problems.
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.
In this math worksheet, learners answer 7 questions having to do with continuous functions, the Squeeze Theorem, and the Product Rule for differentiation.
In this multivariable function activity, students find the limits of a function, identify the domain, and explore continuous functions. This two page activity contains explanations, definitions, and examples. There are approximately four multi-step problems in this activity.
In 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.
In 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.
In this math worksheet, students give examples of functions that will satisfy given conditions. Students tell the tabulations for a given function. Students use the definition of a derivative to compute the inverse of a function. they state the Fundamental Theorem of Calculus and describe its usefulness. Students give an example of a function that can not be integrable.
In this continuity of functions worksheet, students solve calculus function problems. They find the limits and determine when a function is continuous. This one-page worksheet contains 3 multi-step problems.
Practing their functions skills, students solve seven short answer (computation) problems. They tell the points that each function is continuous. The answers to three of the problems are included on the worksheet.
In this functions worksheet, students determine the values of the variables so that the function is continuous for x. They solve one word problem (application problem) related to percents.
In this function worksheet, students determine the limits of functions, sketch graphs, and use the Intermediate-Value Theorem for functions. This two-page worksheet contains twenty-two problems.
Math may have one right answer, but there can be multiple ways to find that answer. Input and output are the foundation of functions, and this activity allows pupils to chose their method to solve for a future output. Bring this activity into your classroom and let your learners practice with graphing, tables, or equations to find the solution from given data. Teacher notes and follow-up questions are provided as well as solutions for the different methods.
Katie won an MP3 player and needs to pick a download site to get some music, is it cheaper to pay the joining fee or pay per song? The task of this problems allows for multiple solution strategies to compare the properties of each function. The answer key is included and shows options for graphing, table, and equations. The facilitator notes provide extra questions to ask your learners along the way to encourage discussion about the topic as a class or within groups.
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 the first problem where multiplication should have been used instead of addition, resulting in the correct answer of 3/16.