Building from the familiar quadratic and cubic functions, students have the opportunity to investigate the properties of power functions, polynomial functions, and rational functions. In particular, students study the nature of maximum and minimum values for these functions, endpoint behavior, the number and nature of their zeros, symmetry in their graphical representations, and the asymptotic relationships they share with other functions. Students examine ways to fit function models to linear, exponential, and polynomial functions using a variety of methods. Using technology, students have the opportunity to investigate the role played by the value of the coefficients in a general cubic function, having studied the same for the quadratic function. Additionally, students should see rational functions in terms of the quotient of two other functions of types already studied.
Students also have an opportunity to fit curves to data using power functions.
This approach foreshadows the ideas of limit and convergence. The sine, cosine, and tangent functions are introduced through periodic phenomena such as the horizontal and vertical projection of a rotating bicycle wheel, or the number of daylight hours for cities at a given latitude. The graphs of these functions are explored using the graphing calculator. As with other functions studied earlier in the course, the questions of domain, range, and elementary transformations of the functions are central to the study. Specific applications of the law of sines and law of cosines are examined.