Question

Select all the relations that are functions (hint: 3 correct answers).

1) (2, 2),(4, 4),(6, 6),(8, 8)
2) (0, 3),(3, 5),(5, 6),(8, 4)
3) (1, 2),(3, 3),(4, 8),(6, 3)
4) (3, 4),(5, 2),(5, 6),(7, 3)

Answer 1

Relations 1, 2, and 3 are functions because in each relation, every x-value is associated with exactly one y-value. Relation 4 is not a function because the x-value 5 is paired with more than one y-value.

Step-by-step explanation:

The student has asked which of the given relations are functions. A function is a special type of relation where each input (x-value) corresponds to exactly one output (y-value). To determine which relations are functions, we need to check if any x-value is associated with more than one y-value in each set of ordered pairs.

• Relation 1: (2, 2),(4, 4),(6, 6),(8, 8) - Each x-value is paired with exactly one y-value; therefore, this is a function.
• Relation 2: (0, 3),(3, 5),(5, 6),(8, 4) - Each x-value is paired with exactly one y-value; therefore, this is also a function.
• Relation 3: (1, 2),(3, 3),(4, 8),(6, 3) - Each x-value is paired with exactly one y-value; therefore, this is a function as well.
• Relation 4: (3, 4),(5, 2),(5, 6),(7, 3) - The x-value 5 is paired with two different y-values (2 and 6), so this is not a function.

Therefore, relations 1, 2, and 3 are the ones that qualify as functions.