Posts Tagged ‘lines’
Thursday, December 31st, 2009
How to Write Step Functions
Description
A detailed tutorial on how to write step functions. Step by step tutorial including several examples of how to write step functions for reference.
Overview
A step function, also called a staircase function, is a finite linear combination composed of several different intervals. They are considered to be a piecewise constant function. The graph of a step function is often expressed as steps, or a staircase, which is how it got its name. It simply looks like several disconnected lines, with alternate open and closed ends so that it easily passes the vertical line test for functions.
Tags: closed, combination, constant, diconnected, discrete math, ends, finite, function, graph, intervals, line, linear, lines, open, piecewise, staircase, step, test, vertical
Posted in Discrete Math | No Comments »
Thursday, December 24th, 2009
Finding the Function of a Directed Graph
Description
A detailed tutorial on finding the function of a directed graph. Step by step tutorial including several examples of finding functions of digraphs for reference.
Overview
A directed graph, more commonly known as a digraph, is the visual representation of a function or of a relation. As in any graph, there are points and lines – called vertices and edges in a digraph. Each edge has an arrow pointing to a vertex. The first vertex – the one the arrow comes from – is the x coordinate of an ordered pair. The second vertex – the one the arrow is pointing to – is the y coordinate of an ordered pair. In the case of double-sided arrows, two ordered pairs are made, with the x and y coordinates switching. This is done for every single vertex and edge on the graph.
Tags: arrow, coordinate. ordered, digraph, directed, discrete math, double, edges, expression, First, function, graph, lines, pair, points, relation, representation, second, side, vertex, vertices, visual, x, y
Posted in Discrete Math | No Comments »
Thursday, November 19th, 2009
The X and Y Axis on a Cartesian Graph
Description
A detailed tutorial of the x axis and the y axis. Step by step tutorial including several examples of the x axis and the y axis for reference.
Overview
The the Cartesian coordinate system, there is an x axis and a y axis. The x axis runs horizontally across the system and all first terms in ordered pairs are x coordinates, from the x axis. The y axis runs vertically across the system and all second terms in ordered pairs are y coordinates, from the y axis. The x and y axis work together to use a pattern of right angles and perpendicular lines in order to find ordered pairs and coordinates of x and y on the graph.
Tags: algebra, angle, axis, basic, cartesian, coordinate, graphing, graphs, horizontal, lines, ordered, pairs, perpendicular, right, system, vertical, x, y
Posted in Algebra | No Comments »
Tuesday, November 17th, 2009
Introduction to Half-Planes
Description
A detailed tutorial on half-planes. Step by step tutorial including several examples of half-planes for reference.
Overview
A half-plane is simply half a plane, that includes all the lines on half of the plane and sometimes the points. If the plane includes the points, it is a closed half-plane. If it doesn’t, then it is an open half-plane. The most common half planes are upper, lower, right, and left planes, where that side of the plane is all that is included. However, there are many other kinds of half planes that are all a variety of diagonal half-planes.
Tags: bottom, closed, Geometry, half, half-plane, left, lines, lower, open, plane, points, region, right, top, upper
Posted in Geometry | No Comments »
Thursday, November 12th, 2009
Definition of Skew Lines
Description
A detailed tutorial on skew lines. Step by step tutorial including several examples and a visual example of skew lines and what they are for reference.
Overview
Skew lines are two lines that do not intersect and are not parallel. In general, these lines have nothing in common. Think of dropping two sticks on the ground from high up. Provided they do not intersect each other (cross or touch each other in any way), those sticks are now a perfect example of skew lines. Typically, these lines are also not found in the same plane. Skew lines can only exist in three or more dimensions.
Tags: arithmetic, common, cross, different, dimension, Geometry, intersect, line, lines, nothing, parallel, plane, skew, three, touch
Posted in Arithmetic | No Comments »
Thursday, November 5th, 2009
Using Tally Marks in Equations
Description
A detailed tutorial om how to use tally marks to solve equations. Step by step tutorial including several examples of tally marks for reference.
Overview
Tally marks are a way of counting that most of us were taught about at a young age – where you count to five by drawing four vertical bars with one diagonal line across them. But tally marks can also be used to help with equations, especially ones with addition and subtraction. As a tally mark is a type of counting numeral that gives you a visual example on solving equations, they can be very useful on simple additon and subtraction problems, as it helps to prove the right answer has been found.
Tags: arithmetic, bar, bars, count, counting, diagonal, five, five-bar, gate, horizontal, lines, numbers, numerals, tally marks, vertical, visual
Posted in Arithmetic | No Comments »
Thursday, November 5th, 2009
Introduction to Projections
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Description
A detailed tutorial on projections. Step by step tutorial including several examples of what a projection is for reference.
Overview
A projection is another term for a transformation. But a projection is a different kind of transformation than a real transformation is. A projection is a transformation of points and lines from one plane to another plane. This is done by connecting corresponding points on the planes with parallel lines. Typically projections are used with vectors, which are entirely composed of points and lines.
Tags: corresponding, dot, infinity, lines, parallel, plane, point, product, projection, transformation, vector
Posted in Algebra | No Comments »
Tuesday, October 6th, 2009
How to Find Oblique Asymptotes
Description
A detailed tutorial on how to find oblique asymptotes. Step by step tutorial including several examples of how to find oblique asymptotes for reference.
Overview
There are several different types of asymptotes. In this tutorial, we will be discussing oblique asymptotes. In order to find the oblique asymptotes of a function, you must first determine if the asymptote slants. If the numerator of a rational function has exactly one degree greater than the denominator, then the function slants and therefore has an oblique asymptote. When you divide the numerator and the denominator, the term or polynomial you get is the oblique asymptote.
Tags: algebra, asymptote, asymptotes, closer, curves, degree, denominator, distance, farther, function, horizontal, infinity, limit, linear, lines, Math, negative, nonlinear, numerator, oblique, origin, polynomial, positive, slant, straight, vertical, zero
Posted in Algebra | No Comments »
Tuesday, September 29th, 2009
How to Find Horizontal Asymptotes
Description
A detailed tutorial on how to find horizontal asymptotes. Step by step tutorial including several examples of how to find horizontal asymptotes for reference.
Overview
There are several different types of asymptotes. In this tutorial, we will be discussing horizontal asymptotes. In order to find the horizontal asymptotes of a function, take the limit of the function to infinity. Every function has a horizontal asymptote if it has a limit to infinity. The limit is your horizontal asymptote.
Tags: algebra, asymptotes, closer, curves, distance, farther, horizontal, infinity, limit, linear, lines, Math, negative, nonlinear, oblique, origin, postive, straight, vertical, zero
Posted in Algebra | No Comments »
Tuesday, September 29th, 2009
How to Find Vertical Asymptotes
Description
A detailed tutorial on how to find vertical asymptotes. Step by step tutorial including several examples of how to find vertical asymptotes for reference.
Overview
There are several different types of asymptotes. In this tutorial, we will be discussing vertical asymptotes. In order to find the vertical asymptotes of a function, we must first determine if there is a vertical asymptote. There is only a vertical asymptote if the limit of the function is equal to positive or negative infinity. If that is true, then the limit will reveal the vertical asymptote.
Tags: algebra, asymptotes, closer, curves, distance, farther, horizontal, infinity, limit, linear, lines, Math, negative, nonlinear, oblique, origin, postive, straight, vertical, zero
Posted in Algebra | No Comments »
