Function Domain and Characteristics

The video tutorial explains how to determine if a relation is a function. A relation is a function if each input has exactly one unique output, meaning the domain cannot repeat. Conversely, a relation is a nonfunction if any input has more than one output. The video provides examples to illustrate these concepts, emphasizing that only the domain matters in determining if a relation is a function, not the range. The tutorial concludes by reinforcing that the domain's uniqueness is the key factor in identifying functions.

Why is it important to determine if a relation is a function?

• To understand the range of a function

• To ensure each input has a unique output

• To find the inverse of a function

• To calculate the slope of a function

What is a key characteristic of a function?

• The domain can repeat

• Each input can have multiple outputs

• The range must be unique

• Each input has exactly one unique output

In the context of functions, what does it mean if the domain repeats?

• The relation is not a function

• The range is incorrect

• The relation is a function

• The function is linear

Which of the following domains indicates a function?

• 1, 2, 2

• 8, 9, 8

• 6, 6, 7

• 3, 4, 5

In the example with domain 1, 3, and 5, why is it considered a function?

• Because the inputs are all positive

• Because the domain does not repeat

• Because the range is unique

• Because the outputs are all negative

Why is the example with domain 1, 1, and 5 not a function?

• Because the outputs are positive

• Because the inputs are negative

• Because the domain repeats

• Because the range repeats

What happens if a domain value has two outputs?

• The function becomes linear

• The range becomes invalid

• It is not a function

• It is still a function

In the example with domain 1, -1, and 1, why is it not a function?

• Because the domain repeats

• Because the outputs are the same

• Because the inputs are opposites

• Because the range repeats

What is the main factor in determining if a relation is a function?

• The intercept

• The slope

• The range

• The domain

Does the range matter when determining if a relation is a function?

• Yes, it must not repeat

• Yes, it must be unique

• No, the range is irrelevant

• No, only the domain matters