Understanding Functions and Bijective Functions

The video tutorial explains function mapping from one set to another, focusing on calculating the total number of possible functions and bijective functions. It introduces the concept of bijective functions, which are both injective and surjective, and explains how to calculate them using the multiplicative principle and permutations. The tutorial provides a detailed walkthrough of these calculations, emphasizing the importance of understanding function properties and permutations.

What is the function f mapping in this context?

• Elements 1 to 5 to elements a to e

• Elements a to e to elements 1 to 5

• Elements 1 to 6 to elements a to f

• Elements a to f to elements 1 to 6

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CCSS.HSF-BF.A.1C

How many total functions are possible without restrictions?

• 1,296

• 720

• 46,656

• 6,000

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CCSS.HSF-BF.A.1C

What is a key characteristic of a bijective function?

• It is only injective

• It is both injective and surjective

• It is only surjective

• It is neither injective nor surjective

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CCSS.HSF-BF.B.4D

How many elements must the domain and codomain have for a function to be bijective?

• The domain must have fewer elements

• The domain must have more elements

• They must have the same number of elements

• The codomain must have more elements

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CCSS.HSF-BF.B.4D

Using the multiplicative principle, how many bijective functions are there?

• 1,296

• 46,656

• 720

• 6

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CCSS.HSF.IF.A.1

CCSS.8.F.A.1

What is the first step in calculating bijective functions using the multiplicative principle?

• Choose 3 outputs for the first input

• Choose 6 outputs for the first input

• Choose 5 outputs for the first input

• Choose 4 outputs for the first input

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CCSS.HSF.IF.A.1

CCSS.8.F.A.1

What is the permutation formula used to calculate bijective functions?

• n factorial divided by n minus k factorial

• n plus k factorial

• n factorial times k factorial

• n minus k factorial

What is the result of 6 permute 6?

• 1,296

• 6

• 720

• 46,656

What is the value of zero factorial?

• 720

• 6

• 1

• 0

Which method confirms the number of bijective functions as 720?

• Addition

• Subtraction

• Permutation

• Multiplication