THE ABSOLUTE VALUE FUNCTION
Let f be a function on to given by: The function just-defined is called the absolute value function. For every x ∈ the image of x under f is denoted by |x|. Thus, The graph of the absolute value functionRead More
HALF IS AS MUCH AS A WHOLE … HOW COME?
The set of all natural numbers, , is a countably infinite set. In fact, . Now, let G be the set of all even natural numbers. Thus, G = {2, 4, 6, 8, 10, 12, …}. Note that G isRead More
THE EQUATION OF ANGLE BISECTOR
In this article, we’ll learn how to determine the equation of the bisector of the angle between two lines whose equations are given. For example, suppose that the equations of lines g and h are and , respectively. As FigureRead More
POWERS AND EXPONENTIAL FUNCTIONS
The readers may find that literatures on mathematics provide various definitions of powers. Some authors do not distinguish the term power from index/exponent. Throughout this article, a power is a mathematical expression in the form of br where . The numberRead More
THE LOGARITHMS
Definition Let , a, b > 0 and b ≠ 1. The logarithm of a to base b, denoted by , is defined as follows. if and only if The number b is called the base of the logarithm, andRead More
A BRIEF INTRODUCTION TO THE NUMBER e
Blindness was not an obstacle for him to deliver magnificent works. Along with his perseverance in studying mathematics, he lost the sight of his right eye and then his left eye as well 31 years later. He discovered a branchRead More
SIMPLIFYING SQUARE ROOTS AND RADICAL FRACTIONS
There are times when we need to simplify a square root such as √500 into a simpler form, that is 10√5. Similarly, the form can be simplified to . Additionally, the radical fraction can be simplified to (√5 – √3).Read More
SOLVING QUADRATIC EQUATIONS BY FACTORIZATION
Quadratic equations have the general form ax2 + bx + c = 0, provided that a ≠ 0. Here are some examples of quadratic equations: x2 – 4x – 5 = 0 [a = 1, bRead More
THE ABC OF THE QUADRATIC FORMULA
A quadratic equation is an equation of the general form ax2 + bx + c = 0 where a ≠ 0. There are several techniques that can be used to find its roots. One of them is by factorization, whichRead More
QUADRATIC FUNCTIONS
A function f from to is called a quadratic function if for some a, b, c ∈ f(x) = ax2 + bx + c, provided that a ≠ 0. The graph of a quadratic function is a parabola, whose shapeRead More