A mapping diagram shows a relation, using arrows, between input and output for the following ordered pairs: (negative 3, negative 4), (0, negative 4), (negative 2, 2), (negative 2, negative 1), (1, negative 3), (3, 7).

Question

Which ordered pair needs to be removed in order for the mapping to represent a function?

(–3, –4)
(–2, –1)
(1, –3)
(3, 7)

Answer 1

In a relation, for it to be considered a function, each input (or x-value) must be associated with exactly one output (or y-value).

In the provided ordered pairs:

• \((-3, -4)\)
• \((0, -4)\)
• \((-2, 2)\)
• \((-2, -1)\) (this is problematic, as -2 is linked to two different outputs: 2 and -1)
• \((1, -3)\)
• \((3, 7)\)

The input \(-2\) is linked to two different outputs (2 and -1). To satisfy the definition of a function, we need to remove one of the pairs containing \(-2\).

Therefore, we can either remove:

• \((-2, 2)\) or
• \((-2, -1)\)

Since the question asks which ordered pair to remove in order for the mapping to represent a function, we can choose either option. However, from the list of options you're provided with, the pair that needs to be removed to ensure the relation is a function is:

\((-2, -1)\)

This ensures that -2 only maps to one output, remaining a valid representation of a function.