Everything in mathematics matches real life. In our real life and in the mysterious world, there are thousands of complex difficult relationships, all of which have functions. There is no such thing as a relationship or relational function. Let me explain the matter with a little example.
Since readers are almost all teenagers, I hear a little love story. Hope you like it.
When a boy and a girl are in a relationship, both parties have to take care of the relationship. Someone's little negligence can ruin the relationship. Friendship, love, whatever the relationship, to survive, we want to trust each other. If this thing does not exist, the strongest relationship will not last. Being in a relationship is never an easy task. Do you know what it means to be like someone, to be like someone else, to have a lot of responsibilities and the ability to endure. A relationship (also called a relationship in mathematics) is real or self-interested only when two people can continue to be relative to each other. Let's make it a little clearer. Suppose a boy is always like a girl's mind, ready to give his all for her. But even after so many things, it can be seen that negligence can come from Opash, even after becoming relative for one, it is seen that the person on Opash does not have the slightest weakness. For some reason, everything becomes worthless. Everything falls apart from the other side. The same is true in mathematics! I mean later. Let's explain with a little example. This time I will try to make the example a little more realistic.
According to what I have understood so far, "a function is a relation where two real things in the mathematical world sustain the relationship."
Let's explain the mathematical relationship a little bit mathematically.
Suppose, y = 2x + 3
Here (in the picture) I have shown a relationship between y and x. Different values of y are available for different values of x. Here the values of x are called domains and the values of y are called codomans. So far but it may or may not be a relationship function. If the function occurs, the codeman is again called the range. Let's make it clearer.
The only function that can happen in real life or the kind of relationship that can actually exist is called a function. Mathematical functions relate to domain ranges. In real life too, let's try to clear the two interrelated issues in a single event by taking the domain range.
Let me remind you first, a function f (x). The domain of that function means a collection of those for which the function is actually set up. If an element of that domain is x_1 then range f (x_1) is clear.
Now what is happening in real life is that a number of cars are participating in a competition called Car Race. Every race car has a speed, doesn't it? But if a car has no speed, just stands on the track, then that car will not be included in the competition. Here we are capturing the cars domain and their speed range. Now let's build some kind of relationship between them.
Here we will indicate the domain of the function i.e., cars c_1 (car number 1), c_2 (car number 2), c_3 (car number 3),… just like in the original race the number is written on each car.
And we have the range of vehicle speeds, I will indicate them as follows, V_1 (Vehicle speed 1), V_2 (Vehicle speed 2), V_3 (Vehicle speed 3),…
The picture shows the relationship between cars and their speed
Picture-1
The first picture shows some cars competing and each of them has a certain speed. The competition is going well. Such incidents happen every day. So if there is such a relationship between the domain ranges of the function, it must be a function. Also here is a range value for a domain of functions so it is a one-to-one function.
Picture-2
The second picture shows the car number 3 Bong 4 running at the same speed. This is not a strange event in a race, it is also a function. However, this function cannot be called one-to-one function as before.
Picture-3
Shown here is each race running at the same speed. This can happen even though it can be a little difficult to know the outcome of the race. However, since such an event is possible, if there is such a relationship between the domain ranges of the function, it is a function.
Picture-4
The race has started but car number 1 is not running, there is no speed, it has not got on the track yet. If I got on the track, I would have written 0. So, it is not possible. Such an event within the domain range cannot be called a function.
Picture-5
In this case no race car is running at v_4 speed. Well there is a race that has such conditions that a car must run at a speed of at least 150 km / h. Never. Then this event is also possible. Such a relationship of domain ranges can also be called a function.
Picture-6
Here it is said that car number 2 is running at the same speed as v_1, v_2 and car number 3 is running at the same speed as v_3, v_4. The same car is moving at two different speeds at the same time. Does that even seem possible? However, such a Gaza incident is not possible, so if such an event occurs within the domain range of a mathematical relationship, it will not be a function.
So you understand that the real thing is that if more than one value of the range is found for a value of a domain in a relationship or not at all, then that relationship cannot be a function. All other cases will function. Simply put, if the relationship is shown with a picture like this, you have to make sure that two arrows never come out of the domain. Nor can it be that no arrow indicating a relationship has come out of the domain.
In the test, it is always said with such pictures which is a function and which is not a function.
Since it is possible to know whether a relation function is possible only by knowing how many values of y are available for x, we can tell by looking at a relation graph whether it will be a function. This will be discussed again in the graph diagram chapter of the function.
