Posts Tagged ‘left’
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 »
Friday, November 13th, 2009
Overview of Negative Slopes
Description
A detailed tutorial on negative slopes. Step by step tutorial including several example problems with negative slopes for reference.
Overview
A negative slope is very similar to a positive slope. It is still in the form of rise over run, and it makes no real difference in an equation if a slope is negative or positive. What it does is change the way you graph it. A positive slope you go up and the to the right. In a negative slope, you will either go up and to the left or down and to the right, depending on if the rise or the run is negative. The main mistake that people make with a negative slope is thinking if they see a negative sign, the slope is definitely negative. This is not true. A negative rise and a negative run actually equals a positive slope, you graph it as going down and going to the left, which still creates a positive slope – and in mathematics, two negatives make a positive.
Tags: diagonal, down, graph, horizontal, left, negative, positive, right, rise, run, slope, up, vertical
Posted in Algebra | No Comments »
Thursday, November 5th, 2009
Main Diagonal of a Matrix
Description
A detailed tutorial on the main diagonal of a matrix. Step by step tutorial including several examples of main diagonals for reference.
Overview
The main diagonal of a matrix is the diagonal that starts at the top left corner, and continues down and to the right one step until either the other corner is reached (square matrices only), the bottom of the matrix is reached, or the right side of the matrix is reached. The main diagonal is also sometimes called the primary diagonal or the leading diagonal
Tags: algebra, bottom, diagonal, leading, left, linear, main, matrices, matrix, primary, regular, right, square, step, top
Posted in Algebra | No Comments »
Thursday, November 5th, 2009
Upper and Lower Triangular Matrices
Description
A detailed tutorial on upper and lower triangular matrices. Step by step tutorial including several examples of triangular matrices for reference.
Overview
A triangular matrix is a kind of square matrix where an element above or below the main diagonal is 0. This gives the true elements of the matrix a triangle shape, which is how it got its name. An upper triangular matrix is sometimes called a right triangular matrix. The matrix is up in the right upper corner, and the 0 element is in the lower left corner. A lower triangular matrix is sometimes called a left triangular matrix. The matrix is in the left bottom corner, and the 0 element is in the upper right corner.
Tags: 0, algebra, bottom, element, left, lower, matrices, matrix, right, square, top, triangle, triangular, upper, zero
Posted in Algebra | No Comments »
Tuesday, November 3rd, 2009
Rule of Sarrus Explained
Description
A detailed tutorial on the Rule of Sarrus. Step by step tutorial including several examples of the Rule of Sarrus and determinants for reference.
Overview
The Rule of Sarrus is a method used to compute the determinant of a 3×3 matrix. Mathematically stated, if you are given a 3×3 matrix, you can compute the determinant by repeating the first two columns of the matrix behind the third column, so that you have 5 columns in a row. This forms a 3×5 matrix. Then you add the products of the diagonals going from top to bottom (left to right), and subtract the products going from bottom to top (left to right). This can also be used for 2×2 matrices, but the rule used is a little different.
Tags: 2x2, 3x3, 3x5, add, algebra, bottom, column, determinant, diagonal, left, matrices, matrix, product, right, row, rule, sarrus, scheme, subtract, top
Posted in Algebra | No Comments »
Thursday, October 22nd, 2009
How to Identify the Phase Shift
Description
A detailed tutorial on the phase shift of a function. Step by step tutorial including several examples of the phase shift of a function for reference.
Overview
The phase shift is another way of saying a horizontal shift – that is, when a graph moves from left to right. If the phase shift is positive, the graph shifts to the left, and if the phase shift is negative, the graph shifts to the right. Finding a phase shift is not difficult – when a value is included with x (instead of included with something relating to x), then a horizontal shift or phase shift will be performed. Simply look at the equation of the function to find the value.
Tags: algebra, equation, function, graph, horizontal, left, negative, phase, positive, right, shift, value, x
Posted in Algebra | No Comments »
Friday, September 11th, 2009
How to Translate Graphs
Description
A detailed tutorial on the translation of graphs. Step by step tutorial including several examples of translating graphs for reference.
Overview
There are different ways to translate graphs, but the easiest way is to memorize the general rules for translation. This tells you what parts of the equation do what to your basic graph. Starting with a graph of y = f(x), these would be your basic rules:
y = f(x – a) moves a units to the right
y = f(x + a) moves a units to the left
y = f(x) + a moves a units up
y = f(x) – a moves a units down
y = f(-x) reflects over the y-axis
y = -f(x) reflects over the x-axis
Reflections are always done before translations, not the other way around, because if you do your translation first you will end up with your shape having the wrong coordinates.
Tags: algebra, down, graph, graphing, graphing techniques, graphs, left, Math, refliection, right, translate, translation, up
Posted in Algebra | No Comments »
