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Functions and mappings

Hi there,


For this question, it asks whether this mapping is one-to-one, many-to-one or one-to-many.

I thought one-to-many, however the solution bank for the textbook (Edexcel) tells me one-to-one.

Does anyone know the correct answer, and could clear this up for me please?

Thank you!

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(edited 3 years ago)
Original post by Dan Silverman
Hi there,


For this question, it asks whether this mapping is one-to-one, many-to-one or one-to-many.

I thought one-to-many, however the solution bank for the textbook (Edexcel) tells me one-to-one.

Does anyone know the correct answer, and could clear this up for me please?

Thank you!


Actually, this is many-to-one.

You can use horizontal/vertical line tests to determine this if you have trouble just by looking at it.

You can learn it here:

https://www.chilimath.com/lessons/intermediate-algebra/vertical-line-test/
https://www.chilimath.com/lessons/intermediate-algebra/horizontal-line-test/

In brief, if your mapping passes the vertical line test, then your mapping is a function (i.e. either one-to-one, or many-to-one).

If your mapping passes the horizontal line test, then your mapping is injective (i.e. one-to-one).

Mappings which pass both tests must necessarily be one-to-one.
(edited 3 years ago)
Original post by RDKGames
Actually, this is many-to-one.

You can use horizontal/vertical line tests to determine this if you have trouble just by looking at it.

You can learn it here:

https://www.chilimath.com/lessons/intermediate-algebra/vertical-line-test/
https://www.chilimath.com/lessons/intermediate-algebra/horizontal-line-test/

In brief, if your mapping passes the vertical line test, then your mapping is a function (i.e. either one-to-one, or many-to-one).

If your mapping passes the horizontal line test, then your mapping is injective (i.e. one-to-one).

Mappings which pass both tests must necessarily be one-to-one.

Thank you! I meant many-to-one but thank you for clearing this up and sharing those links with me. The solution bank for my textbook told me a different answer - confusing me. Have a good evening!

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