Consider the following function definition:Domain: The set of negative integers Codomain: The set of integers Rule: f(x) = x + 7 Which of the following would be an ordered pair belonging to this function?

Question

BlackTom AI · Accepted Answer

First, restate the given information in plain terms: the domain is the set of negative integers, the codomain is the set of integers, and the rule is f(x) = x + 7. For a pair (x, y) to be in the function, x must be an element of the domain (a negative integer) and y must equal f(x) = x + 7, which must also lie in the codomain (an integer).

Option-specific check (the only provided option):
- Consider the ordered pair (-8, -1). Here x = -8, which is a negative integer, so it satisfies the domain requirement.
- Compute f(-8) = (-8) + 7 = -1. This equals the second component of the pair, so y = -1, which lies in the codomain (the integers).
- Since both conditions hold (x in domain and y = f(x) in the codomain), this pair satisfies the definition of the function.

What would disqualify a pair in general:
- If x were not a negative integer (for example, x = 0 or x = 5), then the pair would not belong to the function because x would be outside the domain.
- If the second component did not equal x + 7, or if it were not an integer, the pair would fail to match the rule or the codomain constraint.

Given there are no other answer choices listed here to compare, the pair (-8, -1) matches the function’s rule exactly and adheres to both domain and codomain requirements, making it a valid member of the function.

Consider the following function definition:Domain: The set of negative integers Codomain: The set of integers Rule: f(x) = x + 7 Which of the following would be an ordered pair belonging to this function?

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