Posts Tagged ‘down’
Thursday, December 17th, 2009
The Story of the Infinite Hotel
Description
A detailed tale of the Infinite Hotel. Step by step story including several pictures and an explanation of the Infinite Hotel for reference.
Overview
The Infinite Hotel is a famous math story and puzzle that was thought of by David Hilbert, a German mathematician. Sometimes the Infinite Hotel is called Hilbert’s Paradox of the Grand Hotel. It states that if one person comes into the hotel and all the rooms are full, they can all move down one room and the person can then take the first room. If k number of people come into the hotel and all the rooms are full, everyone can move down k number of rooms to make room for the people that just arrived. And, if double the amount of people that are already there are looking for rooms, everyone in room n can move to room 2n, making room for all the new arrivals in the odd-numbered rooms. This example of the Infinite Hotel can be used in certain forms of mathematical induction, and also in set theory and studies dealing with infinite numbers.
Tags: algebra, arrivals, David Hilbert, double, down, German, grand, Hilbert, hotel, induction, infinite, infinity, k, move, n!, new, numbers, paradox, room, set, space, theory
Posted in Algebra | 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, October 22nd, 2009
How to Identify a Concave Function
Description
A detailed tutorial on concave functions. Step by step tutorial including several examples of concave functions and concave down curves for reference.
Overview
When a function forms the graph of a curve, there are two types of functions it could be: a convex function, or a concave function. In this tutorial, we will discuss concave functions. A concave function is one with the endpoints facing down, forming the shape of an upside down bowl. When looking at the graph of a concave function, we say that it is concave down. Concavity can be found by the second derivative test in calculus.
Tags: Calculus, concave, concavity, convex, curve, derivative, down, endpoint, equation, function, graph, interval, second, test, up
Posted in Calculus | No Comments »
Thursday, October 22nd, 2009
How to Identify a Convex Function
Description
A detailed tutorial on convex functions. Step by step tutorial including several examples of convex functions and concave up curves for reference.
Overview
When a function forms the graph of a curve, there are two types of functions it could be: a convex function, or a concave function. In this tutorial, we will discuss convex functions. A convex function is one with the endpoints facing up, forming the shape of a bowl. When looking at the graph of a convex function, we say that it is concave up. Concavity can be found by the second derivative test in calculus.
Tags: Calculus, concave, concavity, convex, curve, derivative, down, endpoint, equation, function, graph, interval, second, test, up
Posted in Calculus | No Comments »
Thursday, October 8th, 2009
Introduction to Inflection Points
Description
A detailed tutorial on inflection points. Step by step tutorial including several examples of inflection points and how to locate inflection points for reference.
Overview
An inflection point, sometimes also known as a point of inflection, is a point on the graph of a function at which the function changes sign. This means that a concave up curve will become a concave down curve, or a concave down curve will become a concave up curve. Inflection points are also points of local maxima and local minima of a function. There are two ways to categorize inflection points. There are stationary points of inflection, and non-stationary points of inflection. Stationary points are formed when the function is zero, and non-stationary points are when the function is not zero.
Tags: Calculus, concave, curve, down, function, inflection, inflexion, local, Math, maxima, minima, non-stationary, point, saddle-point, sign, stationary, up
Posted in Calculus | 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 »
