Functions of a Real Variable and Drawing Curves — Some properties of functions

About this lesson

This unit introduces students to the properties of functions of a real variable, focusing on symmetry and one-to-one (injective) functions. It begins by explaining symmetry about the y-axis and the origin, then defines even functions (where f(-x) = f(x)) and odd functions (where f(-x) = -f(x)), noting that many functions are neither. The unit provides examples of identifying even and odd functions algebraically and graphically, including power functions, trigonometric functions, and composite functions. It also covers the horizontal line test for determining if a function is one-to-one, with algebraic proofs and graphical examples. Students are expected to classify functions as even, odd, or neither, and to determine if functions are one-to-one using both algebraic and graphical methods. The unit includes exercises that ask students to complete graphs to create even or odd functions and to analyze symmetry and range.