Domain, Kodomain dan Range Suatu Fungsi - Matematika Kelas XI Kurikulum Merdeka

Summary

In this video, the concepts of domain, codomain, and range in functions are discussed with clear examples. The domain is defined as the origin area, consisting of all members of the first set in a function. The codomain is the second set that contains potential results, while the range refers to the actual results, which are the members of the second set that have a corresponding partner in the first set. A practical example is provided, showing how to identify the domain, codomain, and range from an arrow diagram, offering a comprehensive understanding of these essential mathematical concepts.

Takeaways

• 😀 Domain refers to the set of all possible inputs in a function, typically represented by the first set in an arrow diagram.
• 😀 The codomain is the set of all potential outputs of a function, which is the second set in an arrow diagram.
• 😀 The range represents the actual outputs that are mapped from the domain, which is a subset of the codomain.
• 😀 The domain is also known as the 'origin area,' which includes all members of the first set in a function.
• 😀 The codomain is referred to as the 'friend area,' which includes all members of the second set in a function.
• 😀 The range, or 'result area,' only includes elements from the codomain that have a corresponding partner in the domain.
• 😀 Not all elements of the codomain will be part of the range; only those that are linked to an element from the domain are included.
• 😀 In an arrow diagram, the elements from the first set (domain) map to elements in the second set (codomain).
• 😀 The difference between domain, codomain, and range is crucial in understanding how functions map input to output.
• 😀 The function example with sets A = {1, 2, 3} and B = {a, b, c, d, e} illustrates how to identify the domain, codomain, and range in practice.

Q & A

What is the main topic of the video?

The video primarily discusses the concepts of domain, codomain, and range in functions, explaining their definitions and how to determine them through an example.

How is a function represented in the video?

A function is represented using an arrow diagram that maps set A to set B. The elements of set A are paired with the elements of set B to demonstrate the relationships between them.

What is meant by the domain of a function?

The domain of a function refers to the set of all elements in the first set (set A) that are involved in the function. These are the 'origin' elements that map to elements in the second set (set B).

What is the codomain of a function?

The codomain of a function refers to the set of all possible elements in the second set (set B) that could potentially be the result of applying the function. It is also known as the 'friend' area.

What is the difference between the domain and the codomain?

The domain refers to all elements in the first set (set A), while the codomain refers to all possible elements in the second set (set B), even if not all are actually mapped by the function.

What is meant by the range of a function?

The range of a function refers to the set of elements in the second set (set B) that are actually paired with elements in the first set (set A). These are the 'result' elements that have a partner in the domain.

Why is the element '4' not part of the range in the example given?

The element '4' is not part of the range because it does not have a partner in the first set (set A). Only elements in the second set that are paired with elements in the first set are considered part of the range.

What does it mean when we say the range is the 'result area'?

The 'result area' refers to the set of elements in the second set (set B) that are the actual outputs or results of the function, meaning they are mapped from the elements in the first set (set A).

How can we determine the domain, codomain, and range from the given arrow diagram?

From the arrow diagram, we identify the domain by looking at the elements of the first set (set A), the codomain by looking at all the elements of the second set (set B), and the range by looking at the elements in the second set that have a direct connection or mapping from the first set.

What example is used in the video to explain the domain, codomain, and range?

An example function is discussed, where set A contains elements 1, 2, and 3, and set B contains elements a, b, c, d, and e. The video walks through identifying the domain, codomain, and range based on the arrow diagram for this function.