Thursday, October 15th, 2009
Definition of Open and Closed Intervals
Description
A detailed tutorial on open and closed intervals. Step by step tutorial including several examples of open and closed intervals for reference.
Overview
An interval is a set of real numbers, expressed by an ordered pair. There are two types of intervals, open intervals and closed intervals. An open interval is an interval written with parenthesis. It implies that the endpoint is not included in the set. A closed interval is an interval written with brackets. It implies that the endpoint is included in the set. It is possible for one endpoint of an interval to be closed, and for the other to be open.
Tags: algebra, bounded, brackets, closed, coordinates, element, endpoint, interval, Math, open, ordered pair, parenthesis, real numbers, set
Posted in Algebra | No Comments »
Friday, September 25th, 2009
How to Find the Domain & Range of a Function
Description
A detailed tutorial on finding the domain and range of a function. Step by step tutorial including several examples of how to find the domain and range of a function for reference.
Overview
Finding the domain and range is very important when given the graph of a function. The domain is the set of all possible x values of the function, and the range is the set of all possible y values of the function. When given a function, the first one you want to find is the domain. You want to figure out what is allowed for the x value. Typically, the domain ends up being the set of all real numbers, expressed a R. If the x is found in a fraction, it can be the set of all real numbers excluding 0. If the x is found in a square root, it is the set of all real positive numbers. It’s rare for there to only be a few values allowed for the domain. The next one you want to find is range. Very often, range also ends up being the set of all real numbers. But say you know that something has to come out negative, then it would only be the set of all negative numbers. Each function is a little bit different, but finding the domain and range is typically a very straightforward process.
Tags: algebra, domain, fraction, function, graph, Math, negative, positive, possible, range, real numbers, set, square root, values, x, y
Posted in Algebra | No Comments »
Monday, September 21st, 2009
Understanding Real Numbers
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Description
A detailed tutorial on the use and definition of Real Number. Step by step tutorial including several examples of how to use Real Numbers for reference.
Overview
Real numbers is the set of numbers made up of both rational and irrational numbers. This means that if a number can be expressed in a fraction or a non repeating decimal without undefined components, it is a real number. Numbers that don’t fit into this set would include imaginary numbers and those that contain division by 0.
Tags: algebra, irrational numbers, Math, numbers, rational numbers, real numbers
Posted in Algebra, Arithmetic, Math | No Comments »
Tuesday, September 15th, 2009
An In-Depth Look at the Closure Property
Description
A detailed tutorial on how to use the closure property. Step by step tutorial including several examples of how to use the closure property for reference.
Overview
The closure property states that if a and b are both real numbers, then a + b is a unique real number, and a * b is also a unique real number. Basically what the closure property is saying is that if you add or multiply two real numbers, your only possible answer is a real number. The closure property is also saying that the sum or product of two real numbers is unique, meaning there is only one number that it could be.
Tags: add, addition, arithmetic, closure, closure property, Math, multiplication, multiply, product, property, real numbers, sum, unique
Posted in Arithmetic | No Comments »
