What are the domain and range of the function represented by the set of ordered pairs?
[tex]\[
\{(-17,18),(-10,-15),(0,0),(3,-1)\}
\][/tex]

A. Domain: [tex]$\{-17, -10, 0, 3\}$[/tex]
Range: [tex]$\{-15, -1, 0, 18\}$[/tex]

B. Domain: [tex]$-17 \leq x \leq 3$[/tex]
Range: [tex]$-15 \leq y \leq 18$[/tex]

C. Domain: [tex]$\{-15, -1, 0, 18\}$[/tex]
Range: [tex]$\{-17, -10, 0, 3\}$[/tex]

D. Domain: [tex]$-15 \leq x \leq 18$[/tex]
Range: [tex]$-17 \leq y \leq 3$[/tex]



Answer :

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]