Sure! Let's identify the domain of the given function. The domain of a function is the set of all possible input values, or [tex]\( x \)[/tex]-coordinates, that can be plugged into the function.
We are given the function in the form of pairs: [tex]\(\{(1,0),(2,0),(3,0),(4,0),(5,0)\}\)[/tex].
1. First, let's list out the [tex]\( x \)[/tex]-values from each pair:
- From the pair [tex]\((1,0)\)[/tex], the [tex]\( x \)[/tex]-value is 1.
- From the pair [tex]\((2,0)\)[/tex], the [tex]\( x \)[/tex]-value is 2.
- From the pair [tex]\((3,0)\)[/tex], the [tex]\( x \)[/tex]-value is 3.
- From the pair [tex]\((4,0)\)[/tex], the [tex]\( x \)[/tex]-value is 4.
- From the pair [tex]\((5,0)\)[/tex], the [tex]\( x \)[/tex]-value is 5.
2. Next, we collect all unique [tex]\( x \)[/tex]-values together into a set:
[tex]\[\{1, 2, 3, 4, 5\}\][/tex]
So, the domain of the function is the set of all unique [tex]\( x \)[/tex]-values, which is:
[tex]\[ \{1, 2, 3, 4, 5\} \][/tex]
From the given options, the correct one is:
[tex]\[\{1,2,3,4,5\}\][/tex]
