CHAPTER 2 - LINEAR AND QUADRATIC FUNCTIONS

Abstract

This chapter presents the linear and quadratic functions. A function f(x) is called linear if f(x) = ax + b for all real values of x, where a and b are constants. If a = 0, then f(x) = b is a constant function; thus, the class of linear functions includes the class of constant functions. A function f(x) is called quadratic if f(x) = ax2 + bx + c, where a, b, and c are constants. A quadratic function is defined for all values of the independent variable x because ax2 + bx + c is a real number for each real number x. The curve of the function y = f(x) is symmetric in the y-axis if for each x, the value of y at -x is the same as at x; in mathematical notation, f(-x) = f(x). If f(x) satisfies this condition, it is called an even function. The curve y = f(x) is symmetric in the origin if for each x, the value of y at -x is the negative of the value at x, that is, f (−x) = -f(x). If f(x) satisfies this condition, it is called an odd function.