This is a Pre-AP task in which students work with piecewise defined functions that are composed of radical and quadratic functions. Students will begin with the graph of a piecewise function and use the graph to write the function that it represents. They will then evaluate the function at various x-values and determine the average rate of change over a specified interval. The slope function (derivative) is given and students will use this to determine the instantaneous rate of change at a specific point, and then to write the equation of a line tangent to a specific point. Included in this task are 'hint' cards for places in which students frequently have questions. These cards may be used as necessary to give students a hint about how to approach what may be challenging questions.
There is also an assessment task for use after the initial work. In the assessment task students will create and graph piecewise functions that meet specific conditions, evaluate these functions at specific x-values, then use the derivative to write the equation of a line tangent to the curve at a specific point. There is a rubric included with this assignment.
The zip file included:
-Initial Pre-AP assignment as an editable .doc file
-Assessment task as both an editable .doc file and a .pdf file
-Teacher Notes as both an editable .doc file and a.pdf file
-Answer key to initial Pre-AP assignment as a .pdf file