Question

Express the relation in the mapping as a set of ordered pairs.

A) {(−5, 8), (−2, −8), (0, −10), (0, 8), (4, 5)}
B) {(−5, 8), (−2, −10), (0, −10), (0, 8), (4, 5)}
C) {(−5, 8), (−2, −10), (0, −10), (0, 8), (0, 5)}
D) {(−5, 8), (−5, −10), (0, −10), (0, 8), (4, 5)}

Answer 1

The correct set of ordered pairs that represents a relation in the mapping is:

B) {(−5, 8), (−2, −10), (0, −10), (0, 8), (4, 5)}

Answer 2

To determine the correct expression of the relation in the mapping as a set of ordered pairs, we must ensure that each input corresponds to only one output. Upon analysis, Option B is the correct set of ordered pairs that respects this rule.

Step-by-step explanation:

The student is asked to express the relation in the mapping as a set of ordered pairs. When we examine the provided options, it's clear that they are all sets of ordered pairs already. However, we need to determine which one correctly represents the mapping in question. A relation can be expressed as a set of ordered pairs where each pair consists of an input and an output, like (x, y). In mapping, each input can have only one output. This means in our set of ordered pairs, each x-value should be associated with only one y-value.

By analyzing the options given:

• Option A has two pairs with the same first element, (0, −10) and (0, 8), which violates the principle that in a function or mapping, an input cannot map to two different outputs. Therefore, this option is incorrect.
• Option B seems to respect the rule that each input maps to only one output.
• Option C also has a repeat of the first element with (0, −10), (0, 8), and (0, 5), indicating multiple outputs for the same input, which is not allowed.
• Option D repeats the first element (−5, 8) and (−5, −10), which also indicates multiple outputs for a single input and thus is incorrect.

Given the criteria for a proper mapping where each input corresponds to a single output, option B is the correct representation of the relation as a set of ordered pairs.