To determine the domain and range of the function represented by the set of ordered pairs [tex]\(\{(-12,-5),(-10,5),(10,-5),(12,5)\}\)[/tex], we first need to identify where these ordered pairs fall in the context of the function.
Domain:
The domain of a function represents all possible [tex]\(x\)[/tex]-values in the set of ordered pairs. From the given set of ordered pairs, let's extract the [tex]\(x\)[/tex]-values:
1. [tex]\((-12, -5)\)[/tex] ⟹ [tex]\(x = -12\)[/tex]
2. [tex]\((-10, 5)\)[/tex] ⟹ [tex]\(x = -10\)[/tex]
3. [tex]\((10, -5)\)[/tex] ⟹ [tex]\(x = 10\)[/tex]
4. [tex]\((12, 5)\)[/tex] ⟹ [tex]\(x = 12\)[/tex]
Hence, the domain is [tex]\(\{-12, -10, 10, 12\}\)[/tex].
Range:
The range of a function represents all possible [tex]\(y\)[/tex]-values in the set of ordered pairs. From the given set of ordered pairs, let's extract the [tex]\(y\)[/tex]-values:
1. [tex]\((-12, -5)\)[/tex] ⟹ [tex]\(y = -5\)[/tex]
2. [tex]\((-10, 5)\)[/tex] ⟹ [tex]\(y = 5\)[/tex]
3. [tex]\((10, -5)\)[/tex] ⟹ [tex]\(y = -5\)[/tex]
4. [tex]\((12, 5)\)[/tex] ⟹ [tex]\(y = 5\)[/tex]
Hence, the range is [tex]\(\{-5, 5\}\)[/tex].
Now we compare these with the provided options:
A. Domain: [tex]\(\{-5, 5\}\)[/tex]
Range: [tex]\(\{-12, -10, 10, 12\}\)[/tex]
This is incorrect since it swaps the domain and range.
B. Domain: [tex]\(\{-12, -10, 10, 12\}\)[/tex]
Range: [tex]\(\{-5, 5\}\)[/tex]
This matches our determined values.
C. Domain: [tex]\(-12 \leq x \leq 12\)[/tex]
Range: [tex]\(-5 \leq y \leq 5\)[/tex]
While this encompasses all [tex]\(x\)[/tex]- and [tex]\(y\)[/tex]-values, it is not a precise listing of individual domain and range values.
D. Domain: [tex]\(\{10, 12\}\)[/tex]
Range: [tex]\(\{5\}\)[/tex]
This is incorrect since it incompletely lists the domain and range.
Thus, the correct answer is:
B. Domain: [tex]\(\{-12, -10, 10, 12\}\)[/tex]
Range: [tex]\(\{-5, 5\}\)[/tex]
Therefore, the answer to the question is option B.
