Domain and image
Código CM01-E4100-I
VIEW:417 DATA:2020-03-20
Imagine that a car is traveling down a street, and imagine that that car is traveling down the street with the function, "s" of "t" equal to 5 times t, and that time is measured in seconds and the route in meters. In a simpler way, the Domain would be time, and the image would be the route.
Then in the 1 second domain, the car would be in the image 5 meters. And if the domain was 2 seconds, the car would be in the 10 meter image, and if the domain was 3 seconds, the car would be in the 15 meter image.
This is the easiest way I found, to understand what is the domain and image of a function.
In pure mathematics every function f from A to B such that x belongs to A, and y belongs to B such that x and y belong to f Dominion is equal to A, and Image is contained in B.
When we look at mathematical writing, along with the definition speech, it seems to the majority something incomprehensible. But let's understand what this is for. Imagine a Formula 1 race. There is a track, and cars can only drive on that track, and the maximum time for a race is 4 hours. So we have that the Domain is in the period of 4 hours, and the image is in the course of Formula 1.
And what is this knowledge for? Each Formula 1 car is controlled between its position and the time. This control is done in a computer system that manages, for each time domain, an image on the route, to see what is the best way to win the competition.
But it can work for an industry. If the domain is the amount of wheat that is placed at the entrance, the image is the amount of wheat flour that leaves the industry. Let's say that the function of the quantity of wheat is "f" of p, being po weight, of wheat, equal to p divided by 4. So we have to enter 4 kilos of wheat, 1 kilo of flour will come out. So the 4 kilos of wheat is the domain, and 1 kilo of flour is the image. In this way it is possible to control an industry.
Let's do some mathematical analysis.
Let "f" be a function that relates each real number to its opposite. So we can call the domain number x, and so we have that "f" of x is equal to minus x, since minus x is the opposite. So we have that minus x is the image.
Now let's look at the graph, the more the x which is the domain increases, the more the image less x decreases. In a practical way, imagine that a person borrows x money without interest, so the money he receives is the domain, but he now owes x money, that is, the more he borrows the more he owes. And being in debt would be the image. So this graph would be the graph of how much the individual is indebted, in relation to how much he borrows.
See that mathematics can be very useful to understand what happens.
Now let's look at another example. Where the image is your domain's cube. So we have a very interesting graph, which is a property of the potentiation variations, when the domain is in the range of minus 1, and plus 1 it varies very little, but leaving this value it varies a lot.
We can see another one in which the image is the square of the domain minus 1. Here we have a curve called a parabola. Note that the minimum point in the image is -1, because below it there is no more risk. The curve is just above -1. So you can put any number in the domain that the image will never have a value less than -1.
In another example we have that the domain function is the same as the image that is 2, in this case, it doesn't change anything, that is, no matter what the value of the domain, the image will always be 2. Basically this is the most practical understanding it is the domain and image of a function.
Then in the 1 second domain, the car would be in the image 5 meters. And if the domain was 2 seconds, the car would be in the 10 meter image, and if the domain was 3 seconds, the car would be in the 15 meter image.
This is the easiest way I found, to understand what is the domain and image of a function.
In pure mathematics every function f from A to B such that x belongs to A, and y belongs to B such that x and y belong to f Dominion is equal to A, and Image is contained in B.
When we look at mathematical writing, along with the definition speech, it seems to the majority something incomprehensible. But let's understand what this is for. Imagine a Formula 1 race. There is a track, and cars can only drive on that track, and the maximum time for a race is 4 hours. So we have that the Domain is in the period of 4 hours, and the image is in the course of Formula 1.
And what is this knowledge for? Each Formula 1 car is controlled between its position and the time. This control is done in a computer system that manages, for each time domain, an image on the route, to see what is the best way to win the competition.
But it can work for an industry. If the domain is the amount of wheat that is placed at the entrance, the image is the amount of wheat flour that leaves the industry. Let's say that the function of the quantity of wheat is "f" of p, being po weight, of wheat, equal to p divided by 4. So we have to enter 4 kilos of wheat, 1 kilo of flour will come out. So the 4 kilos of wheat is the domain, and 1 kilo of flour is the image. In this way it is possible to control an industry.
Let's do some mathematical analysis.
Let "f" be a function that relates each real number to its opposite. So we can call the domain number x, and so we have that "f" of x is equal to minus x, since minus x is the opposite. So we have that minus x is the image.
Now let's look at the graph, the more the x which is the domain increases, the more the image less x decreases. In a practical way, imagine that a person borrows x money without interest, so the money he receives is the domain, but he now owes x money, that is, the more he borrows the more he owes. And being in debt would be the image. So this graph would be the graph of how much the individual is indebted, in relation to how much he borrows.
See that mathematics can be very useful to understand what happens.
Now let's look at another example. Where the image is your domain's cube. So we have a very interesting graph, which is a property of the potentiation variations, when the domain is in the range of minus 1, and plus 1 it varies very little, but leaving this value it varies a lot.
We can see another one in which the image is the square of the domain minus 1. Here we have a curve called a parabola. Note that the minimum point in the image is -1, because below it there is no more risk. The curve is just above -1. So you can put any number in the domain that the image will never have a value less than -1.
In another example we have that the domain function is the same as the image that is 2, in this case, it doesn't change anything, that is, no matter what the value of the domain, the image will always be 2. Basically this is the most practical understanding it is the domain and image of a function.
BUSCADAVERDADE
Visite o nosso canal youtube.com/buscadaverdade e se INSCREVA agora mesmo! Lá temos uma diversidade de temas interessantes sobre: Saúde, Receitas Saudáveis, Benefícios dos Alimentos, Benefícios das Vitaminas e Sais Minerais... Dê uma olhadinha, você vai gostar! E não se esqueça, dê o seu like e se INSCREVA! Clique abaixo e vá direto ao canal!
Saiba Mais
-
Nutrição
Vegetarianismo e a Vitamina B12 -
Receita
Como preparar a Proteína Vegetal Texturizada -
Arqueologia
Livro de Enoque é um livro profético?
Tags
functions, domain, image, graphs, equations, algebra