Understanding Functions: Injective, Surjective, and Bijective

The video tutorial explores the concepts of injective, surjective, and bijective functions. It provides definitions and examples to help determine if a function is injective, surjective, both, or neither. The tutorial includes three examples, each illustrating a different type of function: one that is only surjective, one that is only injective, and one that is neither. The explanations focus on the relationships between the domain and codomain elements to identify the function type.

What is a function called if every element of the codomain is the image of at most one element from the domain?

• Neither

• Surjective

• Bijective

• Injective

What is a bijective function?

• A function that is only surjective

• A function that is only injective

• A function that is neither injective nor surjective

• A function that is both injective and surjective

Which type of function ensures that every element of the codomain is mapped by at least one element from the domain?

• Injective

• Surjective

• Bijective

• None of the above

In the first example, why is the function not injective?

• Because it is not surjective

• Because it has repeated elements in the codomain

• Because it is bijective

• Because it misses elements in the codomain

In the first example, what type of function is demonstrated?

• Bijective

• Surjective

• Neither

• Injective

In the second example, why is the function considered injective?

• Every element of the codomain is an image of at least one element from the domain

• Every element of the codomain is an image of at most one element from the domain

• The function is bijective

• The function is surjective

Why is the second example not surjective?

• It misses elements in the codomain

• It has repeated elements in the codomain

• It is injective

• It is bijective

In the third example, why is the function neither injective nor surjective?

• It is only surjective

• It is only injective

• It is both injective and surjective

• It has more elements in the codomain than the domain

What is the main reason the third example is not injective?

• It is surjective

• It is bijective

• It misses elements in the codomain

• It has repeated elements in the codomain

What is the main reason the third example is not surjective?

• It has repeated elements in the codomain

• It is bijective

• It misses elements in the codomain

• It is injective