Question

x = {(2, 3), (2, 4), (2, 5), (2, 6)} is x a function and why?
○ no, there is a limited number of ordered pairs in this list.
○ yes, there is more than one ordered pair in this list.
○ yes, no two ordered pairs in this list has the same second element.
○ no, each ordered pair in this list has the same first element.

Explanation:

Step1: Recall function definition

A function is a relation where each input (first element of ordered pair) has exactly one output (second element of ordered pair).

Step2: Analyze the given relation

In \( x = \{(2, 3), (2, 4), (2, 5), (2, 6)\} \), the first element of each ordered pair is \( 2 \). So the input \( 2 \) is mapped to multiple outputs (\( 3, 4, 5, 6 \)).

Step3: Evaluate each option

• Option 1: The number of ordered pairs doesn't determine if it's a function. Eliminate.
• Option 2: Having more than one ordered pair isn't the definition of a function. Eliminate.
• Option 3: The condition about second elements is irrelevant for the function definition (it's about first elements having unique outputs). Eliminate.
• Option 4: Since the same first element (\( 2 \)) has multiple second elements, it's not a function. This matches the function definition violation.

Answer:

D. No, each ordered pair in this list has the same first element.