Understanding Functions: Surjective and Injective

The video introduces key mathematical terminology related to functions, focusing on surjective (onto) and injective (one-to-one) functions. It explains the concepts of domain, co-domain, image, and range, and provides examples to illustrate how these functions map elements between sets. The video also distinguishes between surjective and injective functions, highlighting their unique properties and how they relate to the co-domain and range.

What is the primary role of a co-domain in a function?

• It is the set of all possible mappings.

• It is the set of possible outputs for the function.

• It is the set of inputs for the function.

• It is the set of all elements that are not mapped.

Which of the following best describes a surjective function?

• No elements in the co-domain are mapped to.

• Every element in the co-domain is mapped to by at least one element in the domain.

• Every element in the domain maps to a unique element in the co-domain.

• Some elements in the domain do not map to the co-domain.

In a surjective function, what is the relationship between the image and the co-domain?

• The image is always larger than the co-domain.

• The image is equal to the co-domain.

• The image is unrelated to the co-domain.

• The image is a subset of the co-domain.

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

What is another term used for the image of a function?

• Mapping

• Range

• Co-domain

• Domain

What defines an injective function?

• Every element in the domain maps to a unique element in the co-domain.

• Every element in the co-domain is mapped to by at least one element in the domain.

• Some elements in the co-domain are not mapped to.

• No elements in the domain map to the co-domain.

In an injective function, what happens if two elements in the domain map to the same element in the co-domain?

• The function remains injective.

• The function is no longer injective.

• The function becomes surjective.

• The function becomes bijective.

How can you identify a non-injective function?

• By finding elements in the domain that map to the same element in the co-domain.

• By ensuring every element in the co-domain is mapped to.

• By checking if the image equals the co-domain.

• By verifying that no elements in the domain map to the co-domain.

What is the main difference between surjective and injective functions?

• Injective functions map every element in the co-domain to a unique element in the domain.

• Surjective functions map every element in the domain to a unique element in the co-domain.

• Injective functions ensure every element in the co-domain is mapped to, while surjective functions ensure unique mappings from the domain.

• Surjective functions ensure every element in the co-domain is mapped to, while injective functions ensure unique mappings from the domain.

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CCSS.HSF.BF.B.3

What happens to the injectiveness of a function if two elements in the domain map to the same element in the co-domain?

• The function becomes bijective.

• The function becomes surjective.

• The function remains injective.

• The function loses its injectiveness.

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CCSS.HSF-BF.B.4D

If a function is both surjective and injective, what is it called?

• Transitive

• Reflective

• Symmetric

• Bijective

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CCSS.HSF-BF.B.4D