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Functions and Relationships (Analytic Geometry)

An equation of 2 or more variables representing a rule of correspondence or relationship between variables. This matching rule indicates the values \u200b\u200bthat should or can take the variables. The last variable value must be calculated, we can not arbitrarily determine, since it is restricted by the value of other variables.



relationships or correspondence rules are the most common of 2 variables, because they can be graphed on the Cartesian plane. In these relationships we choose to our liking the value of a variable (independent variable) and calculate the value of the other (dependent variable). By custom and convenience have been chosen as the variables are x for the independent variable and for the dependent variable. Thus will have the same letters as in the x-axis and axis Cartesian Plane.



If for every value we chose (independent variable) are 2 or more values \u200b\u200bof another variable (dependent variable) have a relationship . But, if for every value we chose (independent variable) is only one value of another variable (dependent variable) have a FUNCTION.



functions, like equations, are classified by grade, type of terms and number of variables. When classified by its degree is very common to assign names related to its graph. Thus, the first degree usually call linear, because its graph is a straight line to the second level functions typically call Dish, because its graph is a parabola.



The following are examples of names of different functions depending on the type of its terms: Logarithmic, Exponential, Rational, Hyperbolic, Elliptic, asymptotically, Periodicals, etc..

To see an animated explanation and exercises on these issues, download the following files:



Functions: Definition and classification. click here to download .


To open this file you need Microsoft Power Point or Apple Computer Inc. Keynote.

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Equations and Classification (Algebra)

are equalities in Equations which has one or more unknowns, ie, have one or more numbers that do not know its value within the operations described in equality.



The formal definition of equation is as follows: "An equation is a comparison by an equal sign, two algebraic expressions." These algebraic expressions written representation of operations arithmetic between numbers (if you know its numeric value) and variables or unknowns (do not know their numeric value.)



The equations are classified by the degree of its terms and the number of unknowns different in them. This classification reflects the way how to solve different types of equations.

To see an animated explanation and exercises on these issues, download the following files:




Equations: Definition and classification. To download click here .


To open this file you need Microsoft Power Point or Apple Computer Inc. Keynote.

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Girth (Analytic Geometry)

The circle is a "picture" we all know. Is a line drawing of a closed curve "gives a perfect lap." The definition of "formal" Circumference is:

"A circle is the set of all points of the plane that are equidistant from another point on the plane called the Center"

This means that each point on the circle has the same distance to the center . This distance is called the radius of the circle. Thus, when you draw a circle with a compass, the opening of this bar is exactly what measures the radio.



circumference part of the "cone" or "conical projections." They are called because they arise from the conical intersection of a plane with a cone (actually double cone, the cones joined by their end). All these conical are generated from a particular form of an equation of 2 variables of grade 2. Thus, the equation of a circle is second degree in x and second grade and .



To see an animated explanation of the circumference and exercises, download the following files:

General Form Equation of Circle: click here to download .


Canonical Form of the Equation of the Circle: click here to download .


Symmetric Form of the Equation Circumference: click here to download .


normal or parametric equation of the circle: click here to download .


To open these files you need Microsoft Power Point or Apple Computer Inc. Keynote.



To graph a circle from the equation must be found several pairs of values. Each pair is a "coordinate". These points together and you get the chart.



plot lines to help you download the following graph: GrafCircunf1.0


need to run this plotter LabVIEW Run-Time Engine 7.0 - Windows/2000/98/ME/NT/XP.

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The line (Analytic Geometry)

There are many definitions for the line, each of these definitions has to do with the context. The definition in Euclidean geometry and we know from elementary:

"A straight line which lies evenly with the points that are in it"

from the Book of Euclid's Elements.

In this line we were taught that extends indefinitely in both directions, which is infinite and never "turn." In short it is a line "straighter" and infinite.



The definition of "formal" Straight in Analytic Geometry is as follows:

"A straight line is the set of all points of the plane where the coordinates of each point obey a first-degree relationship "

Analytic Geometry For the importance of the line is to find the equation that" generates "and this equation is the" relation of first grade, "says the definition.



In conclusion, the line is a function first grade of 2 variables. This function or line equation can be written in several different ways and each way (or form of the line) has a different name. These ways are the following 6 (Further explanation is found in the following files to download):

General Form of Equation of Straight: click here to download .


Canonical Form of the Equation of Straight: click here to download .


Point-Slope Equation of Straight: click here to download .


two-point form of the Equation of Straight: click here to download .


Symmetric Form Equation of Straight: click here to download .


Normal Form of the Equation of Straight: click here to download . Exercises


"Equation of the Line": click here to download .


To open these files you need Microsoft Power Point or Apple Computer Inc. Keynote.



To plot a straight from the equation must find pairs of values. Each pair is a "coordinate". These points together and you get the chart.



plot lines to help you download the following graph: GrafRecta1.0

need to run this plotter LabVIEW Run-Time Engine 7.0 - Windows/2000/98/ME/NT/XP .

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Graph of a Function (Analytic Geometry)

The graph of a function is the geometric representation in a Cartesian plane of a function of 2 variables (equation 2 unknowns). The geometric representation is a figure drawn in the plane obtained by joining together many consecutive points as they appear to be a continuous line.



To find the graph of a function of 2 variables (usually x and and P) are calculated values \u200b\u200bof the variables (for each value of x a corresponding value of and ) forming pairs numbers. Each pair of values \u200b\u200brepresents a point in the Cartesian plane. When you have enough points you can get by joining lines to form figures features each type of function. Find



figure obtained from an equation or find the equation that describes a geometric figure are the objectives behind Analytic Geometry. It helps for the geometry and algebra, although the latter is the most important for analytic geometry.

To see an animated explanation and exercises on these issues, download the following files:



Graph of a function. click here to download .


To open this file you need Microsoft Power Point or Apple Computer Inc. Keynote.

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Plano Cartesian (Analytic Geometry)

The Cartesian Plane is a very useful tool in many daily activities. Serves as a reference in any plane, eg the plane (or floor) in our city.



it is called Cartesian plane invented by the philosopher and mathematician René Descartes (1596-1650).



The Cartesian Plane is constructed by drawing two number lines, one horizontal and the other vertical, they cross each other in their respective zeros, the zero crossing is called origin and each of the lines are called Cartesian axes or coordinate axes.



horizontal line in the positive numbers to the right of the origin and the negative to the left of the origin. In the vertical line are positive numbers above the origin and negative below the origin. In addition, you can also draw lines parallel to the axis, thus forming a grid.



The usefulness and versatility of the Cartesian Plane is that it can locate a point without confusion with just two numbers. These two numbers are called coordinates or ordered pair and the order is ( x , and ).

To see an animated explanation and exercises on these issues, download the following files:



The Cartesian plane. click here to download .


To open this file you need Microsoft Power Point or Apple Computer Inc. Keynote.