Determine if the set of ordered pairs is a relation or a function. Select all that apply.

Question

(2,2),(3,2),(4,3),(5,4)

Answer 1

To determine if the set of ordered pairs $(2,2),(3,2),(4,3),(5,4)$ is a relation or a function, we need to understand the definitions of both:

1. Relation: A relation is any set of ordered pairs. Thus, any set of pairs is considered a relation.

2. Function: A function is a specific type of relation where each input (the first element of the pair) corresponds to exactly one output (the second element of the pair). This means that no two ordered pairs can have the same first element with different second elements.

Now, let's examine the ordered pairs given:

• $(2,2)$
• $(3,2)$
• $(4,3)$
• $(5,4)$

Here, the first elements are 2, 3, 4, and 5. Each of these first elements is unique and corresponds to only one second element:

• 2 corresponds to 2
• 3 corresponds to 2
• 4 corresponds to 3
• 5 corresponds to 4

Since no first element repeats with a different second element, the set does satisfy the criteria for being a function.

In conclusion:

• The set is a relation (because all sets of ordered pairs are relations).
• The set is also a function (because each input corresponds to exactly one output).

Thus, the correct options are:

• It is a relation.
• It is a function.