Algebra, Relations and Functions — Sign of a Function

About this lesson

This unit teaches students how to investigate the sign of a function, meaning to determine for which values of the variable x the function's output is positive, negative, or zero. It covers three types of functions: constant functions (f(x)=c), linear functions (f(x)=bx+c), and quadratic functions (f(x)=ax²+bx+c). For each type, the text explains how to determine the sign based on the function's rule and graph, including cases for quadratic functions where the discriminant is positive, negative, or zero. The unit includes worked examples, graphical representations, and exercises for students to practice determining signs and graphing functions. By the end, students should be able to determine the sign of a given function, represent it graphically, and apply this to prove properties like the nature of roots of equations.