Understanding Functions: Injective, Surjective, and Bijective

This video tutorial explains how to determine if a function is injective, surjective, bijective, or neither. It provides definitions and characteristics of each type of function, followed by examples to illustrate these concepts. The video covers four examples: a surjective function, an injective function, a function that is neither, and a bijective function, explaining the reasoning behind each classification.

What is a key characteristic of an injective function?

• Every element of the domain maps to a unique element in the codomain.

• Every element of the codomain is mapped by at least one element of the domain.

• The function has repeated elements in the codomain.

• The function is both injective and surjective.

In an injective function, what is true about the elements of the codomain?

• They are missing from the range.

• They are all covered by the domain.

• They are repeated in the range.

• They are not repeated in the range.

Which statement is true for a function that is only injective?

• It is both injective and surjective.

• It has missing elements in the codomain.

• It has repeated elements in the codomain.

• It covers all elements of the codomain.

Which of the following is true for a surjective function?

• It has missing elements in the codomain.

• Every element of the codomain is mapped by at least one element of the domain.

• It is neither injective nor surjective.

• It has repeated elements in the domain.

In a surjective function, what is the relationship between the domain and codomain?

• The codomain has more elements than the domain.

• Every element of the codomain is covered by the domain.

• The domain has more elements than the codomain.

• The function is injective.

What is a characteristic of a function that is only surjective?

• It is neither injective nor surjective.

• It is both injective and surjective.

• It has missing elements in the codomain.

• It has repeated elements in the codomain.

What happens in a function that is neither injective nor surjective?

• All elements of the codomain are covered.

• The function is bijective.

• There are missing elements in the codomain.

• There are repeated elements in the codomain.

Which of the following is true for a bijective function?

• It is both injective and surjective.

• It is only injective.

• It is neither injective nor surjective.

• It is only surjective.

What is a defining feature of a bijective function?

• It is only surjective.

• Every element of the codomain is mapped by exactly one element of the domain.

• It has repeated elements in the codomain.

• It has missing elements in the codomain.

What is the relationship between the domain and codomain in a bijective function?

• Every element of the codomain is mapped by exactly one element of the domain.

• The codomain has more elements than the domain.

• The function is only injective.

• The domain has more elements than the codomain.