Let's identify the domain and range of the function represented by the set of ordered pairs \(\{(-17,18),(-10,-15),(0,0),(3,-1)\}\).
Step 1: Identify the Domain
The domain of a function is the set of all possible input values (or \(x\)-values in the ordered pairs).
Given ordered pairs:
[tex]\[
(-17, 18), (-10, -15), (0, 0), (3, -1)
\][/tex]
The \(x\)-values are:
[tex]\[
-17, -10, 0, 3
\][/tex]
So, the domain is:
[tex]\[
\{-17, -10, 0, 3\}
\][/tex]
Step 2: Identify the Range
The range of a function is the set of all possible output values (or \(y\)-values in the ordered pairs).
Given ordered pairs:
[tex]\[
(-17, 18), (-10, -15), (0, 0), (3, -1)
\][/tex]
The \(y\)-values are:
[tex]\[
18, -15, 0, -1
\][/tex]
So, the range is:
[tex]\[
\{-15, -1, 0, 18\}
\][/tex]
Step 3: Match the Domain and Range to the Given Options
- Option A:
- Domain: \(\{-17, -10, 0, 3\}\) – Matches
- Range: \(\{-15, -1, 0, 18\}\) – Matches
- Option B:
- Domain: \(-17 \leq x \leq 3\) – \(\mathbf{Incorrect}\) (Domain should be a set of discrete values)
- Range: \(-15 \leq y \leq 18\) – \(\mathbf{Incorrect}\) (Range should be a set of discrete values)
- Option C:
- Domain: \(\{-15, -1, 0, 18\}\) – \(\mathbf{Incorrect}\) (These are the range values, not domain)
- Range: \(\{-17, -10, 0, 3\}\) – \(\mathbf{Incorrect}\) (These are the domain values, not range)
- Option D:
- Domain: \(-15 \leq x \leq 18\) – \(\mathbf{Incorrect}\) (Domain should be a set of discrete values)
- Range: \(-17 \leq y \leq 3\) – \(\mathbf{Incorrect}\) (Range should be a set of discrete values)
The correct answer is:
[tex]\[
\boxed{\text{A}}
\][/tex]
