How to tell the difference between onto and one to one functions

The video tutorial explains the concept of functions, focusing on the definition and examples of functions, non-functions, one-to-one functions, and onto functions. It highlights the importance of each element in the domain mapping to a unique element in the range for a function to be valid. The tutorial also distinguishes between one-to-one and onto functions, providing examples and non-examples to clarify these concepts. Finally, it discusses the characteristics of functions that are both one-to-one and onto.

What is the defining characteristic of a function in terms of domain and range?

• Each element in the domain pairs with multiple elements in the range.

• Each element in the domain pairs with exactly one element in the range.

• Each element in the range pairs with multiple elements in the domain.

• Each element in the range pairs with exactly one element in the domain.

In a one-to-one function, what is the relationship between elements in the domain and range?

• Each element in the domain pairs uniquely with one element in the range.

• Each element in the range pairs with multiple elements in the domain.

• Each element in the domain pairs with multiple elements in the range.

• Each element in the range pairs uniquely with one element in the domain.

Which of the following is NOT a characteristic of a one-to-one function?

• Each element in the range is paired with a unique element in the domain.

• No two elements in the domain pair with the same element in the range.

• Each element in the domain pairs uniquely with one element in the range.

• Multiple elements in the domain can pair with the same element in the range.

What is required for a function to be considered onto?

• Every element in the domain is paired with multiple elements in the range.

• Every element in the range is paired with multiple elements in the domain.

• Every element in the range is paired with an element in the domain.

• Every element in the domain is paired with an element in the range.

Which statement is true for a function that is both one-to-one and onto?

• Each element in the domain pairs with multiple elements in the range.

• Each element in the range pairs with multiple elements in the domain.

• Each element in the domain pairs uniquely with one element in the range, and every element in the range is paired with an element in the domain.

• Each element in the range pairs uniquely with one element in the domain, and every element in the domain is paired with an element in the range.