Determine whether the relation is a function. Explain. {(2,5),(4,−2),(3,3),(5,4),(−2,5)}2,5,4,-2,3,3,5,4,-2,5 Multiple choice question.A)Yes; for each element of the domain, there is only one element of the range.B)Yes; for each element of the range, there is only one element of the domain.C)No; the elements –2, 3, 4, and 5 are in both the domain and the range.D)No; the element 5 occurs twice in the range.
Question
Determine whether the relation is a function. Explain. {(2,5),(4,−2),(3,3),(5,4),(−2,5)}2,5,4,-2,3,3,5,4,-2,5 Multiple choice question.A)Yes; for each element of the domain, there is only one element of the range.B)Yes; for each element of the range, there is only one element of the domain.C)No; the elements –2, 3, 4, and 5 are in both the domain and the range.D)No; the element 5 occurs twice in the range.
Solution
The correct answer is A) Yes; for each element of the domain, there is only one element of the range.
Here's why:
A function is a relation in which each element of the domain is paired with exactly one element of the range. The domain is the set of all first elements (x-values) of the ordered pairs, and the range is the set of all second elements (y-values).
Looking at the given relation {(2,5),(4,−2),(3,3),(5,4),(−2,5)}, we can see that each x-value (the domain) is paired with exactly one y-value (the range).
2 is paired with 5, 4 is paired with -2, 3 is paired with 3, 5 is paired with 4, and -2 is paired with 5.
No x-value is paired with more than one y-value, so this relation is a function.
The other options are incorrect because:
B) This is not the definition of a function. A function is defined by each element of the domain having one element in the range, not the other way around.
C) It doesn't matter if elements are in both the domain and the range. What matters is that each element of the domain is paired with exactly one element of the range.
D) It doesn't matter if an element occurs more than once in the range. What matters is that each element of the domain is paired with exactly one element of the range.
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