Understanding Functions and Relations

The video tutorial reviews Form 4 Chapter 1 on Functions, covering basic concepts such as representing relations using sets, arrow diagrams, ordered pairs, and graphs. It explains the terms domain, codomain, and range, and discusses objects and images in relations. The tutorial explores different types of relations, including one-to-one, many-to-one, one-to-many, and many-to-many, and defines functions as a special type of relation. Examples and practice questions are provided to reinforce understanding.

Which of the following is NOT a way to represent a relation?

• Arrow diagram

• Bar chart

• Ordered pairs

• Graph

What is the term for the set of all possible outputs in a relation?

• Domain

• Range

• Codomain

• Image

In a relation, what do we call the set of elements that are actually mapped to by elements of the domain?

• Range

• Object

• Codomain

• Domain

Which type of relation has each object in the domain mapping to exactly one image in the codomain?

• Many-to-many

• One-to-many

• Many-to-one

• One-to-one

What type of relation is it when multiple objects map to the same image?

• One-to-many

• Many-to-one

• One-to-one

• Many-to-many

Which of the following is a characteristic of a function?

• Each image in the codomain has exactly one object

• Each image in the codomain has multiple objects

• Each object in the domain has exactly one image

• Each object in the domain has multiple images

Why is a relation with one object having two images not considered a function?

• It violates the one-to-many mapping rule

• It violates the many-to-many mapping rule

• It violates the many-to-one mapping rule

• It violates the one-to-one mapping rule

In the example question, what is the object of the image 4?

• B

• A

• C

• D

What is the range of the relation in the example question?

• {1, 2, 3}

• {2, 3, 4}

• {1, 3, 4}

• {1, 2, 4}

What type of relation is demonstrated in the example question with sets A and B?

• One-to-one

• Many-to-many

• Many-to-one

• One-to-many