RELASI DAN FUNGSI | DOMAIN, KODOMAIN, RANGE - Matematika Kelas 8 SMP

Summary

In this educational video, the teacher explains the concepts of domain, codomain, and range in the context of relations between sets. Using examples and visual aids, the video clarifies that the domain represents the set of all possible inputs, the codomain is the set of all potential outputs, and the range is the actual set of outputs that are mapped from the domain. The teacher also demonstrates how to create a two-fold relation between two sets and identifies the range from this relation. The lesson is aimed at helping students better understand these fundamental concepts in mathematics.

Takeaways

• 😀 Understanding the concept of 'domain': It refers to the set of all elements in the source set (set A) that are related to elements in the target set (set B).
• 😀 'Codomain' refers to the entire set of potential outputs (set B) that can be related to the inputs from the domain.
• 😀 The 'range' refers to the subset of the codomain that actually has relationships with elements from the domain.
• 😀 The domain is typically represented on the left side of the relational diagram, while the codomain is shown on the right.
• 😀 Example: If the relation is from set A (0, 2, 4, 5, 6, 8, 10) to set B (0, 1, 2, 3, 4, 5, 6), the domain is the set A.
• 😀 Codomain is the entire set of possible outputs, represented by set B in this case, including all elements from 0 to 6.
• 😀 The range is determined by the elements in set B that are actually paired with elements in set A, such as (0, 1, 2, 3, 4, 5).
• 😀 To create a relation, you identify the connections based on the given condition, like 'double of A'. For instance, 0 is twice 0, 2 is twice 1, etc.
• 😀 The process of creating a relational diagram involves pairing elements of set A with the corresponding elements of set B that satisfy the condition.
• 😀 The video emphasizes practicing and repeating the learning process at home to ensure better understanding of concepts like domain, codomain, and range.

Q & A

What is the main topic of the video?

The main topic of the video is learning about relations and functions, specifically focusing on domain, codomain, and range.

What is the definition of 'domain' in the context of relations?

The domain of a relation is the set of all elements from the first set (set A) that are related to elements in the second set (set B). It is represented on the left side of the relation diagram.

What does 'codomain' mean in a relation?

The codomain of a relation is the set of all possible elements that could potentially be related to the elements in the domain. It is represented on the right side of the relation diagram.

How is 'range' defined in the video?

The range of a relation consists of the elements in the codomain that are actually related to elements in the domain. It can be seen as the actual outcomes or values resulting from the relation.

In the example provided in the video, what are the sets A and B?

In the example, set A is {0, 2, 4, 5, 6, 8, 10}, and set B is {0, 1, 2, 3, 4, 5, 6}.

How do you determine the domain from the example?

The domain is determined by identifying the elements from set A that are involved in the relation. In this case, the domain is {0, 2, 4, 6, 8, 10}.

What is the codomain in the given example?

The codomain is the entire set B, which is {0, 1, 2, 3, 4, 5, 6}.

What was the relationship described as 'two times' (dua kalinya) in the example?

The relation described as 'two times' means that each element of set A is related to an element in set B where the element of set B is twice the value of the element in set A.

What is the range in this specific example of the relation?

The range in this example consists of the elements in set B that have a matching element in set A. The range is {0, 1, 2, 3, 4, 5}.

Can an element from set A be in the range without having a matching element in set B?

No, an element from set A cannot be in the range without having a corresponding element in set B. The range consists of the elements from set B that are paired with elements from set A.