Understanding Domain, Range, and Functions

The video tutorial explains how to determine the domain and range of a relation and assess if it is a function. It uses two examples of relations given as sets of ordered pairs. The first example shows a relation that is not a function because some inputs have multiple outputs. The second example demonstrates a relation that is a function, where each input has exactly one output. The tutorial also illustrates how to map relations to visually determine if they are functions.

What is the domain of a relation?

• The set of all ordered pairs

• The set of all possible outputs

• The set of all possible inputs

• The set of all functions

Which of the following is true about a function?

• Each input can have multiple outputs

• Each input has exactly one output

• Each output can have multiple inputs

• Each output has exactly one input

In the first example, what is the domain?

• Three, five, seven

• Five, seven

• Negative three, negative two

• Negative three, negative two, negative one

Why is the first example not a function?

• Each input has exactly one output

• Some inputs have multiple outputs

• All outputs are the same

• There are no inputs

What does mapping a relation help to determine?

• The range of the relation

• The number of ordered pairs

• The domain of the relation

• If the relation is a function

In the second example, what is the range?

• Four and five

• Three, five, seven

• Negative five, negative three, negative two

• One and four

Why is the second example a function?

• There are no repeated inputs

• All outputs are different

• Each input has exactly one output

• Each input has multiple outputs

What is the domain in the second example?

• One and four

• Three, five, seven

• Negative three, negative two

• Negative five, negative three, negative two, negative one, one

In the mapping of the second example, what is observed?

• Each element in the range has multiple arrows

• Each element in the range has exactly one arrow

• Each element in the domain has exactly one arrow

• Each element in the domain has multiple arrows

What is the significance of mapping in understanding functions?

• It lists all possible outputs

• It shows the number of ordered pairs

• It visually confirms if each input has one output

• It determines the range