Non-Linear Behavior

In this module students explore a variety of non-linear functions. Each type of function has an application to motivate the use of it. Students learn to solve these equations graphically and algebraically. Lesson 1 Quadratic Functions and Parabolas Students explore the power of the parameters in a quadratic function to control the shape of the graph. They also look at second differences of quadratic data sets. Nitty Gritty: Solving for any variable in an equation. Lesson 2 Products and Factoring Students learn to factor quadratics (of the form x2 + bx + c), and the relationship of the factors to the x-intercepts. Lesson 3 Solving Equations Students solve quadratic equations by graphing and by using the quadratic formula. Lesson 4 Complex Numbers The imaginary unit is defined. An application of complex numbers to electronics is explored. Nitty Gritty: Operations on complex numbers. Lesson 5 Cubic Graphs and Equations This lesson develops a feel for the graphs of cubic equations much like Lesson 1 does for quadratics. Students describe the characteristics of the graph and then explore how the parameters change the shape of the graph. Lesson 6 Modeling Cubic Data Cubic regression is used to model data sets. Students explore x- and y- intercepts of cubic graphs. Lesson 7 Patterns in Cubic Data Students discover that third differences are constant in cubic functions. Students use their accumulated knowledge to determine if data sets are linear, quadratic or cubic. Lesson 8 Radical Functions Students are introduced to two applications which use radical equations: scaling and a certain application of the Pythagorean Theorem. Students learn to solve radical equations. Lesson 9 Absolute Value Functions Absolute value functions are introduced through the application of tolerance of resistors. Students learn to solve absolute value equations and inequalities. Lesson 10 Rational Functions Students explore rational functions through the application of the increased cost of removing a higher and higher percent of a pollutant. Students also learn to solve certain types of rational functions. Nitty Gritty: Solving rational equations algebraically. Lesson 11 Sinusoidal Functions Students use the sine function to describe periodic behavior of the sun and moon, as well as tides. Compare this module to traditional course topics in the Matrix of Course Competencies. If one of the lessons has a link, you can preview that lesson. Other modules: Beat Ratios Functions Exp. Growth Data & Graphs Representing Data Finance Geometry Sampling Non-linear Behavior Linear Behavior Sets and Logic Patterns Probability Systems Right Tri. Trig.