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Question

how do I determine if these two relation problems are a function. Problem number 1 is (4,5),(3,-2),(-2,5),(4,7) Second problem is (4,-2),(-4,-2),(9,-2),(0,-2). Thanks.

Answer 1

a function only occurs when the x variable (domain) does not repeat. so for example, your first problem.... (4,5) (3,-2) (-2, 5) (4,7) There are two "4's" in the domain in sets 1 and 4. This means that it IS NOT a function. However, if the sets were as so: (2,5) (3,-2) (-2, 5) (4,7) then it would be a function. Therefor the second problem you have listed is a function.

Answer 2

Recall that a function is a rule that yields a single output number for every valid input number.



Observe {(4, 5), (3, -2), (-2, 5), (4, 7)}. For (4, 5) and (4, 7), x is 4 (input number), but there are two different y-values (output numbers); hence, this problem is not a function, but a relation.



Observe {(4, -2), (-4, -2), (9, -2), (0, -2)}. All input values (x) are different. From the information we are given, we can conclude this problem is a function.

Answer 3

Problem 1 is not a function either of x or y. A function must have a unique value of the dependent variable for each value of the independent variable. In this problem, there are duplicated values both of x and y so no function exists.



Problem 2 is a function y = f(x), because a unique value of y exists for each value of x. x ≠ f(y) because duplicate values of x exist for given values of y.