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from Ideas and Projects that Work: Part 2
In response to the calculus reform movement in the mid-1990s, we wanted to find a way to prepare students for a calculus course that was more conceptual, contained more real-life applications, and required students to view functions in multiple representations. With the aid of an NSF grant (DUE-9354741) we set out to write projects that would have students solve interesting, real-life problems that involved multiple representations as well as multiple topics from a precalculus course. These 26 projects were eventually published under the title, Projects for Precalculus [1] and could be used as a supplement to any precalculus course.
We, along the with the publisher, thought it would be a good idea to write a textbook based on these projects. Using some of the same philiosophy from our projects, we set out to write Precalculus: A Study of Functions and Their Applications [2]. We wanted this to be a non-traditional precalculus text that treats functions as the object of study while focusing on important mathematical concepts. We did this by introducing each of the basic types of functions (linear, exponential, logarithmic, periodic, and power) early in the book rather than relegating each type to a separate chapter. Doing so allows us to emphasize the commonalities and differences between the various types of functions. The properties of each type of function are developed throughout the remainder of the text. This leads to a natural review as students build on their understanding of functions.
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