Pengertian Fungsi - Matematika Kelas XI Kurikulum Merdeka

Okay, Assalamualaikum warahmatullahi wabarakatuh. Okay, friends, welcome back to the lesson video of my book, Mathematics. In this video, we will discuss one subject in the 11th grade for the Ganjil semester, where maybe friends who have applied for a bachelor's degree in school.

So the first material we will discuss is about the understanding of functions. What and how are the functions? Let's discuss it.

Okay, before discussing the function, of course we need to know what is called a relationship. Maybe you still remember the material in yesterday's SMP about relationships. What is a relationship? Well, a relationship is

a rule that puts a member of the assembly 1 to another assembly. This is called a relation, a rule that puts a member of the assembly 1 to another assembly. The relationship between the two assemblies can be stated in three ways, usually with a pan-reference diagram,

whether a series of even pairs or can also be with the Cartesian diagram, maybe friends often see this, which is usually a Cartesian diagram, then it is called a relationship, okay, for the panag diagram, what is the shape?

usually the form is like this, the first combination for example X with its members ABC with then the second combination, namely the Y combination, with members 1 and 2, usually there is a hot sign like this, then this is the form of the relationship in the pan diagram, okay, then

Then, the order pair. The order pair, we just have to make it in the order pair, x, y, usually, from the existing panagrave. Let's try to pay attention. The existing panagrave, there is a, yes. How many pairs? The pair is with two, yes. So, we write in the curve,

a.2 where a is the first member of the union, 2 is the second member of the union. The pair means a is paired with 2. Okay, then the pair

the next pair we see here there is B, B is paired with 1, so we write again B comma 1 and the last one there is C, C is also paired with 1, so we write C comma 1, like this, which means the pair of numbers in order, okay, then

The third, the Cartesian Diagram. Now, you all know the diagram. The diagram is usually like this. There are x-axis and y-axis. Now, let's go to the first member of the equation.

which is ABC means it is in the root of X, yes, consider it like this, then the second component is the Y component with the component 12 means it is in the root of Y12, then we will attach it according to the pan diagram and the orderly pair that was there,

Now, let's move on to the pair of sequence. We have analyzed that the first pair is A and 2. So, we see here, in the x-axis, A is paired with 2. So, we draw a line like this.

That's the first pair. Then, what else? B, paired with 1. That means the shape is like this, roughly. Then the third, C paired with 1 as well. Then the shape is more or less like this. That's the Cartesian diagram.

So these three shapes, the Pan-Diagram, the Comparative Couple, and the Cartesian Diagram, are called relationships. Okay, that's it. So you have to understand what a relationship is before you can enter the function. Okay, we've discussed relationships. So we just need to discuss functions. What are functions?

So, it's almost the same. So, the function is a relation. But, for

The function itself is more specific. Here are the conditions. That is, one member from one group goes to another member of the group. So the couple has rules, not a set. That is what is called a function.

That's the understanding, then the function is usually stated in the form of f = y This is a function symbol, where f is the function, x is the input variable

and y is the output variable or the output. For more clarity, the function is usually described as a machine. More or less like this, there is an input as the x variable.

There is the function of f and there is the output of fx. For example, in everyday life, there are many. One of them is, for example, we have a grapefruit, we put it in the blender,

A grape juice. This is what is called a function. There was a grape as an input, the blender as a function, then the juice, the blender result was the output. This is one of the functions in everyday life and there are still many other examples.

Okay, hopefully up to here the understanding of relation and function can be understood and differentiated What does the function mean? What is the relation like? Okay, is it clear? Clear Okay, after we know the understanding of the function, now we will

find out which one is a function and not a function. Because earlier we discussed that the relation and function are actually related to each other, only the difference is that the function is more specific. So if you want to illustrate the relationship between functions and relations can be understood through the following image.

The simple explanation is like this, so all functions must be related, all functions must be related, but not all relationships are functions, because what function was it?

Yes, there are conditions. What does it mean? To make it clearer, pay attention to the following pan-diagram. We use the pan-diagram. There is the first diagram, the second, and the third. We try to analyze from the three pan-diagrams, which are the relationship and function,

And which one is a relation but not a function? Okay, let's go back, let's remember first, what function did we understand? Function is a relation that connects one member of a group to another member of a group. So for the first diagram,

There is the first set as X, where the members are A, B, C and the second set is Y with the members 1, 2, 3. All of them already have a couple. Is this a function? From the understanding that exists, let's see first. Here the explanation is to connect one member from one set exactly to another set member, so that

The first diagram is a relation and also a function. Why? Because each member of the X-collection, the first collection, has exactly one pair of members of the Y-collection. That is, it is in accordance with the definition of the existing function. So we say, this first diagram is a relation and also a function.

Because if a diagram is a function, then it must also be a relation. But not all relations are functions. Now the second one, let's try to analyze it first. There is the first collection as X, where the members are A, B, C. And the second collection, the members are 1 and 2.

From the existing image, is this second pan diagram a function or not? It's a relation but not a function. Why is that? It's true. Because in this second pan diagram, there is one member of the X group or the first group that doesn't have a partner. So, this second pan diagram,

It includes a relationship because there is a relationship between the first and second union But it does not meet the requirements as a function That is, all members of the first union must have a partner Here there is an X union member, that is C There is no partner, so this is said to be not a function

can yes? yes, it can then the third the third is this how about the third is it a function or not? yes? no, yes so it remains a relationship but it is not a function how come? because all

the member of the union has a partner. Yes, he has a partner, but he is not in accordance with the existing conditions. Exactly one. Let's see here. Here is one member of the X union who has more than one partner in the Y union. Let's see here. B. The partner has two. One and...

So this does not meet the requirements for a function. Okay, it's clear, right? For the simpler one, it's like this. The function must have a partner and loyal.

It means faithful, one member of the assembly can only choose one couple. See the first example, A couple 2, B couple 3, C couple 1. It means you have to be faithful.

If there is a couple, it must be faithful. Then the second. What is the second? No, you can't be a couple. That means the first member of the assembly cannot be a couple. Everyone must have a couple. Here, the first member of the assembly, C, does not have a couple. It's a couple. That means he is not a function. Okay. So, it must be faithful. Then, you can't be a couple. Then,

The third one is that it is not allowed to be in pairs. So, it is not allowed for the first member of the group to have two pairs. Like here, the member of the group B has two pairs. So, it is not allowed to be in pairs. So, it is necessary to be loyal, not allowed to be in pairs, and not allowed to be in pairs. That's for the easier language. Regarding what is the function.

Okay, it's clear, it's clear here. We have discussed about understanding what is a relationship, what is a function, and differentiate which one is a function and not a function. Hopefully this explanation can be understood. For more clarity, you can work on the following question practice. Pay attention to the following image. This is the diagram.

Cartesius, yes, make it in the pan-H diagram and the sum of the order of the numbers, then determine whether the relationship in the Cartesius diagram is a function or not a function, yes, please work on it with understanding, yes, and the example that we have discussed earlier, you can share the answer in the comments column, okay?

Okay, that's what we can discuss, hopefully useful and can be understood later in the explanation of other materials in the next video. Okay, stay excited and always perform well.