Question

determine whether the relation is a function. give the domain and the range of the relation.

\\(\\{(5,2),(5,7),(6,2),(6,7)\\}\\)

is this a function?
yes
no

the domain is \\(\\{\quad\\}\\)
(use a comma to separate answers as needed.)

the range is \\(\\{\quad\\}\\)
(use a comma to separate answers as needed.)

Explanation:

Determine if the relation is a function

A relation is a function if each element in the domain (the first coordinate \(x\)) maps to exactly one element in the range (the second coordinate \(y\)).
Given relation:

$$ \{(5,2), (5,7), (6,2), (6,7)\} $$

The input \(5\) maps to both \(2\) and \(7\).
The input \(6\) maps to both \(2\) and \(7\).
Since at least one input maps to multiple outputs, the relation is not a function.

Find the domain of the relation

The domain is the set of all first coordinates (\(x\)-values) from the ordered pairs.

$$ \text{Domain} = \{5, 6\} $$

Find the range of the relation

The range is the set of all second coordinates (\(y\)-values) from the ordered pairs.

$$ \text{Range} = \{2, 7\} $$

Answer:

Question 1

• Yes
• No (Correct answer)

Question 2

The domain is {<blank>5, 6</blank>}

Question 3

The range is {<blank>2, 7</blank>}