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This is an engaging card sort activity for studying the intervals of concavity and inflection points of given functions. The functions (common and composite) include polynomials, radical, exponential, logarithmic, trigonometric and inverse trigonometric expressions. They are specially selected so that each function has not more than one inflection point.

Activity Directions: Students determine the intervals of concave up/concave down and the inflection points of each of 12 given functions. They are also given 16 cards each with a statement written on it. The statements concern the concavity and inflection points of the given functions and are true or false. Partners are asked to use their studies on the functions to verify the statements and sort the cards into two groups - “TRUE” and “FALSE”. Thus students do comparative analysis of the functions.

This product can be possibly used as an independent practice, as a partner or a group activity (groups of 3 and 4).

Student recording sheet and all answer keys are provided.

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