Precalculus concepts become clear using multiple representations. Instruction is therefore aimed to show the subject from many angles; illustrations include algebraic, graph-based, and real-world examples and feature the use of the graphing calculator as a calculation and visualization tool on advanced forms of algebraic math.
Students will use polynomial, rational, and algebraic functions to write functions (in standard forms) and draw graphs to solve world problems, to find inverse and composite functions, and to analyze functions and graphs. Course topics start with sets, real numbers, complex numbers, and functions. Then, students will explore properties and graphs of polynomial functions and equations, rational functions, exponential, and logarithmic functions. Additional topics include sequences and series, modeling data with linear and non-linear functions.
Mathematical Lens: Using photos of amusement park rides, water fountains, landscape, house, etc., students model the functions that the shapes of the objects represent
Families of Graphs: Students identify the domain, range, intercepts, zeros, asymptotes, and points of discontinuity of functions. (Use paper and pencil methods and graphing calculators.)
Solve word problems involving applications of logarithmic and exponential functions.
M&M Activity: Using M&Ms, students will generate data to explore exponential growth and decay.
Helicopter Rotors Activity: Using cut-out paper models of short and long rotors, students will compare drop times and model functions.
“Shockwave” activities that illustrate real-time correlations between equations and graphs designed to help students visualize and experiment with the graphs of functions, systems, and complex numbers.
Writing: Explain the use the properties of the number systems and order of operations to justify steps of simplifying functions and solving equations.
Examples of exponential growth and decay occur often in the real world. In the world of finance, for example, there are savings accounts, mortgages, automobile loans. Population growth and the half-lives of radioactive material also provide numerous real world examples of exponential growth and decay. Students will research on selected real-life situation that models exponential growth or exponential decay. Students will produce data through sampling and experiment, organize the data obtained, and explain what information is revealed by their data (i.e., look for patterns and deviations from patterns.