Practice questions
- Is the relation {(2, 5), (3, 7), (4, 1), (8, 1)} a function?
A. The relation is a function because no element of the range is paired with more than one element of the domain. B. The relation is a function because no element of the domain is paired with more than one element of the range. C. The relation is NOT a function because 1 is paired with both 4 and 8. D. The relation is NOT a function because no element of the domain is paired with more than one element of the range. E. The relation is NOT a function because 2 is paired only with 5.
- Does the following mapping represent a function?A. It does represent a function because each number in the domain is paired with at least one number in the range. B. It does represent a function because each number in the range is paired with at least one number in the domain. C. It does NOT represent a function because 2 is paired with both 1 and 12. D. It does NOT represent a function because 5 is paired with both 7 and 10. E. It does represent a function because no number is listed more than once in the left column.
Answers and explanations
- The correct answer is Choice (B). None of the domain numbers (first numbers in the ordered pairs) are paired with more than one range element. In other words, no first number is repeated with a different second number, so the relation is a function.
- The correct answer is Choice (D). The domain element 5 is paired with 7 and 10. It's therefore paired with more than one range element, so it isn't a function. Choices (A), (B), and (E) are incorrect because they have the wrong conclusion and false definitions of function. Choice (C) has the right conclusion but a false definition.