Question

Which of the following relations represents a function?

A) (1,0),(3,0),(1,1),(3,1),(1,3)
B) (1,1),(2,2),(3,3),(4,4),(6,8)
C) (2,7),(6,5),(4,4),(3,3),(2,1)
D) (9,-3),(9,3),(4,2),(4,2),(0,0)

Answer 1

Option B (1,1),(2,2),(3,3),(4,4),(6,8) is the relation that represents a function because each input is paired with only one output.

Step-by-step explanation:

A function is a relation in which each input (often represented as x) is paired with exactly one output (often represented as y). To determine which of the given relations represent a function, we check for unique x-values:

• A) (1,0),(3,0),(1,1),(3,1),(1,3) - Not a function because the input '1' is paired with multiple outputs (0, 1, 3).
• B) (1,1),(2,2),(3,3),(4,4),(6,8) - Is a function because each input is paired with exactly one output.
• C) (2,7),(6,5),(4,4),(3,3),(2,1) - Not a function because the input '2' is paired with two different outputs (7 and 1).
• D) (9,-3),(9,3),(4,2),(4,2),(0,0) - Not a function because the inputs '9' and '4' are each paired with multiple outputs.

Therefore, the relation that represents a function is Option B.