Função 04: Domínio, Contradomínio e Imagem

Summary

In this video, the speaker explains the concept of functions in mathematics, specifically focusing on the relationship between two sets, A and B. Set A contains elements 1, 2, and 3, while set B contains 2, 4, 6, 8, and 10. The speaker highlights that a function maps each element in set A to one and only one element in set B. The domain of the function is all the elements in set A, and the codomain includes all elements in set B. The image of the function includes elements 2, 4, and 6, which are connected to elements from set A. The video aims to clarify the basic structure of functions and how to identify them.

Takeaways

• 😀 The video explains the process of understanding and working with functions, specifically focusing on domain, co-domain, and image.
• 😀 The function is presented as a relationship between two sets: set A (with elements 1, 2, and 3) and set B (with elements 2, 4, 6, 8, and 10).
• 😀 A function is defined as a relation where each element in set A is linked to exactly one element in set B.
• 😀 To determine whether a relation is a function, ensure that every element of set A is paired with exactly one element in set B.
• 😀 The domain of a function consists of all elements of set A, which are 1, 2, and 3 in this case.
• 😀 The co-domain of the function includes all elements of set B, which are 2, 4, 6, 8, and 10.
• 😀 The image of a function is the set of elements in set B that are linked to elements in set A.
• 😀 In the given example, the image of the function consists of the elements 2, 4, and 6 from set B.
• 😀 The video emphasizes the importance of checking if the function follows the rules of associating each element in set A with one and only one element in set B.
• 😀 The video concludes with a reminder that the domain, co-domain, and image are key concepts when working with functions and understanding their structure.

Q & A

What is the main topic of the video script?

The main topic of the video script is about understanding mathematical functions, focusing on concepts such as domain, codomain, and image of a function.

What is the role of the domain in a function?

The domain of a function consists of all the elements from the first set (set A) that are mapped to elements in the second set (set B). In this script, the domain includes the elements 1, 2, and 3.

What is the definition of a function according to the script?

A function is defined as a relation where every element in the domain (set A) is associated with exactly one element in the codomain (set B).

What is the codomain in the function described in the video?

The codomain of the function is the set B, which consists of the elements 2, 4, 6, 8, and 10.

How can you identify if something is a function?

To identify if something is a function, ensure that each element in the domain is associated with exactly one element in the codomain. This is verified by checking that no element in the domain is linked to more than one element in the codomain.

What does the script mention about the relationship between sets A and B in a function?

The script explains that in a function from set A to set B, every element in set A must be connected to one and only one element in set B.

What is meant by the term 'image' in the context of a function?

In the context of a function, the 'image' refers to the set of elements in the codomain (set B) that are associated with the elements of the domain (set A). In this case, the image is the set {2, 4, 6}.

What are the steps mentioned to analyze a function in the video?

The video mentions two main steps: first, verify whether the given relation is a function, and second, identify the domain, codomain, and image of the function.

What is the domain of the function discussed in the script?

The domain of the function is the set A, consisting of the elements 1, 2, and 3.

How does the script suggest checking the image of a function?

To check the image of a function, identify which elements of the codomain (set B) are connected to the elements in the domain (set A). In this case, the image consists of the elements 2, 4, and 6 from set B.