What is the domain of [tex]\{(1,2),(-5,7),(4,1),(0,0)\}[/tex]?

A. [tex](-\infty, \infty)[/tex]
B. [tex]\{-5,0,1,4\}[/tex]
C. [tex]\{0,1,2,7\}[/tex]
D. 4



Answer :

To determine the domain of the set of points \(\{(1,2),(-5,7),(4,1),(0,0)\}\), we need to identify all the first elements (or x-coordinates) in these ordered pairs.

Let's list the points and their x-coordinates:
- Point \((1,2)\) has an x-coordinate of \(1\).
- Point \((-5,7)\) has an x-coordinate of \(-5\).
- Point \((4,1)\) has an x-coordinate of \(4\).
- Point \((0,0)\) has an x-coordinate of \(0\).

So, the x-coordinates from the given set of points are \(\{1, -5, 4, 0\}\).

The domain of the set of points is therefore \(\{-5, 0, 1, 4\}\).

Now, let's match this with the given choices:
- \( (-\infty, \infty) \) implies all real numbers, which is not our list.
- \(\{-5, 0, 1, 4\}\) matches our domain exactly.
- \(\{0, 1, 2, 7\}\) does not match our domain.
- The choice \(4\) is ambiguous and does not relate to the domain of the points.

Given our analysis, the correct answer is:
\(\{-5, 0, 1, 4\}\).

Therefore, the numerical result is:
[tex]\[ \boxed{2} \][/tex]