Real Functions and Graphing Curves — Even and odd functions

About this lesson

This unit introduces students to the concepts of symmetry in the graphs of real functions, focusing on symmetry around the y-axis and around the origin point. It defines even functions as those where f(-x) = f(x) for all x in the domain, with graphs symmetric about the y-axis, and odd functions as those where f(-x) = -f(x), with graphs symmetric about the origin. The unit explains that many functions are neither even nor odd, and emphasizes that the domain must contain both x and -x for a function to be classified as even or odd. It provides examples of investigating functions algebraically and graphically, including polynomial, trigonometric, and radical functions, and states important properties about sums and products of even and odd functions. Students practice identifying even, odd, or neither functions from given formulas and graphs, and complete graphs to achieve symmetry. By the end, students should be able to determine whether a function is even, odd, or neither, both algebraically and graphically, and understand the relationship between symmetry and function type.