Final answer:
After evaluating each provided relation, Relation A and D are the ones that meet the criteria of a function, where each x-value is paired with a unique y-value, while Relation B and C have repeated x-values associated with different y-values, hence are not functions.
Step-by-step explanation:
To determine which of the given relations is a function, we must remember that in a function, each input (x-value) must be paired with exactly one output (y-value). Let's analyze each of the given relations:
- Relation A: (5, -17), (4, 4), (13, 17) - Here, each x-value is unique and is associated with exactly one y-value. Therefore, Relation A is a function.
- Relation B: (8, 13), (-2, 3), (8, 19) - Here, the x-value of 8 is associated with two different y-values (13 and 19). This violates the definition of a function. Hence, Relation B is not a function.
- Relation C: (20, 18), (-10, 12), (20, 7) - Similar to Relation B, the x-value of 20 is paired with two different y-values (18 and 7), making Relation C not a function.
- Relation D: (3, 1), (4, 3), (-13, 16), (-13, 17) - Although the x-value of -13 is associated with two different y-values, this does not affect the definition of a function since the y-values can repeat as long as each x-value has a unique pair, which it does here. Thus, Relation D is a function.
In summary, Relations A and D are functions, while Relations B and C are not.