Understanding Functions

This video tutorial introduces the concept of functions, explaining their definition, notation, and key components such as domain, codomain, and range. It provides examples of functions, including integer and finite set functions, and highlights the differences between codomain and range. The tutorial also discusses examples of rules that do not qualify as functions due to multiple outputs, such as phone numbers.

What is the term used for the set of all possible outputs of a function?

• Domain

• Codomain

• Range

• Image

What is the image of an input in a function?

• The domain of the function

• The input itself

• The codomain of the function

• The output corresponding to the input

In the context of functions, what is the difference between codomain and range?

• Codomain is the set of inputs, range is the set of outputs

• Codomain and range are the same

• Codomain is the set of actual outputs, range is the set of all possible outputs

• Codomain is the set of all possible outputs, range is the set of actual outputs

In the function f(n) = 3n, what is the range?

• All real numbers

• Integer multiples of 3

• All natural numbers

• All integers

For the function g, which maps {1, 2, 3} to {a, b, c}, what is the range?

• {a, c}

• {a, b, c}

• {b, c}

• {a, b}

What distinguishes the function h from the function f, even though they share the same rule?

• Different range

• Different domain and codomain

• Different rule

• Different notation

Why is the rule f(n) = n/2 not considered a function when mapping natural numbers to natural numbers?

• It has multiple outputs for some inputs

• It has no outputs for some inputs

• It is not defined for all inputs

• It has outputs not in the codomain

Why can't a person's phone number be considered a function when using people as the domain?

• People can have multiple phone numbers

• People do not have phone numbers

• Phone numbers are not unique

• Phone numbers change frequently

What is the key requirement for a rule to be considered a function?

• Every input must have exactly one output

• Every output must have at least one input

• Every output must have exactly one input

• Every input must have at least one output

What happens if a phone number is shared by multiple people in terms of function definition?

• It remains a function

• It is not a function

• It becomes a one-to-one function

• It becomes a valid function