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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.

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.

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A detailed tutorial on how to find the interquartile range. Step by step tutorial including several examples of the interquartile range for reference.

The interquartile range is the range of the data between the lower or first quartile and the upper or third quartile. The interquartile range is not the whole data set – it is actually only half of the data set, although not a common half – the first and last quarter of the data is not included in the interquartile range. To find the interquartile range, all you must do is find all the quartiles, and then find the different between the upper quartile and lower quartile.

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A detailed tutorial on the definition of a quartile. Step by step tutorial including several examples of the definition of a quartile for reference.

A quartile is a value that separates out statistical data. There are three quartiles, and they work together to separate data out into four different parts. The first quartile, called Q1, is the lower quartile. It is the 25th percentile of data – that is, the median of the median of the total amount of data, and the lowest count in a data set. The second quartile, called Q2, is the median of the entire data set. It is sometimes referred to as the middle value. The third quartile, called Q3, is the upper quartile. It is the 75th percentile of data – that is, the median of the median of the total amount of data, and the highest count in a data set.

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A detailed tutorial on higher order derivatives. Step by step tutorial including several examples of higher order derivatives for reference.

A higher order derivative is a derivative with a power other than one – that is, a derivative is referred to as a first derivative, and the higher order derivatives are a second derivative, third derivative, etc. The second derivative is the derivative of the first derivative, and the third derivative is the derivative of the second derivative. When you know all the rules of taking derivatives, taking second and third derivatives are simple. Simply take the derivative and pretend it is another equation. When you go up beyond the third derivative this can get more challenging, as there will be many more parts to the equation.

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A detailed tutorial on the domain of relations. Step by step tutorial including several examples of the domain of relations for reference.

The domain of a relation is denoted as Dom(R) and looks like a normal set. For each ordered pair in a relation, there are two endpoints, x and y. The domain is the set of all x endpoints – that is to say, all the endpoints that come first in the ordered pair. If you are taking the domain of the inverse of a relation, then that would be all the y endpoints. When writing the domain, the notation used is just the normal notation, not the ordered pair notation.

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A detailed tutorial of the definition of an abscissa. Step by step tutorial including several examples of the definition of an abscissa for reference.

An abscissa is not a term commonly heard in math, but it is something that most of us are familar with. An abscissa is the first number or element  in an ordered pair – pair implying that there are only two values. A well known example is a Cartesian coordinate (x, y). “x” is the abscissa in this case.

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Description

This video shows the correct way to multiply binomials together using the FOIL technique. A helpful hint for seeing if you matched up the terms correctly is given in the video. Content is laid out in an organized manner.

Overview

FOIL is a basic math function that stands for First, Outside, Inside, Last. It is like the Order of Operations – it gives you a set order to solve problems in. FOIL is used when you multiply two binomials together. Binomials are sets of parenthesis that have two added or subtracted numbers with variables in them. Here is an example of a problem that would need FOIL:

(a + b) (x – y)

You would use FOIL to multiply together different parts of the problem. We will highlight the parts of the problem in their correct order:

First: (a + b) (x – y)

Outside: (a + b) (x – y)

Inside: (a + b) (x – y)

Last: (a + b) (x - y)

Notice that the addition and subtraction signs are grouped with the last term in each set of parenthesis – this is very important if you expect to get the right answer. So, our problem can be simplified by writing it this way:

(a + b) (x – y) = (a * x) + (a * -y) + (b * x) + (b * -y)