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What is the range of the following relation:
[tex]\[ (9, -2), (4, 3), (8, 10), (-4, 8) \][/tex]

A. [tex]\[ -4, 4, 8, 9 \][/tex]
B. [tex]\[ -2, 3, 8, 10 \][/tex]
C. [tex]\[ (9, -2), (4, 3) \][/tex]
D. [tex]\[ (8, 10), (-4, 8) \][/tex]

Sagot :

GinnyAnswer
To determine the range of the given relation:
[tex]\[ (9, -2), (4, 3), (8, 10), (-4, 8) \][/tex]

we need to extract the second elements (or [tex]\( y \)[/tex]-coordinates) from each ordered pair. The range in a set of ordered pairs is the set of all [tex]\( y \)[/tex]-values that appear as the second component in any of the pairs.

Let's go through each pair one by one:

1. For the pair [tex]\( (9, -2) \)[/tex], the [tex]\( y \)[/tex]-component is [tex]\(-2\)[/tex].
2. For the pair [tex]\( (4, 3) \)[/tex], the [tex]\( y \)[/tex]-component is [tex]\(3\)[/tex].
3. For the pair [tex]\( (8, 10) \)[/tex], the [tex]\( y \)[/tex]-component is [tex]\(10\)[/tex].
4. For the pair [tex]\( (-4, 8) \)[/tex], the [tex]\( y \)[/tex]-component is [tex]\(8\)[/tex].

Collecting all these [tex]\( y \)[/tex]-values, we get:
[tex]\[ -2, 3, 10, 8 \][/tex]

Hence, the range of the relation [tex]\((9, -2), (4, 3), (8, 10), (-4, 8)\)[/tex] is:
[tex]\[ -2, 3, 10, 8 \][/tex]

Thus, the correct answer is:

B. [tex]\(-2, 3, 8, 10\)[/tex]
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