To determine the domain of the given function [tex]\(\{(3,-2), (6,1), (-1,4), (5,9), (-4,0)\}\)[/tex], we need to identify all the possible [tex]\(x\)[/tex]-values in the ordered pairs, which are the inputs of the function.
Here are the steps:
1. List the x-coordinates: Extract the [tex]\(x\)[/tex]-values from each ordered pair.
[tex]\[
(3,-2) \rightarrow x=3, \quad (6,1) \rightarrow x=6, \quad (-1,4) \rightarrow x=-1, \quad (5,9) \rightarrow x=5, \quad (-4,0) \rightarrow x=-4
\][/tex]
2. Form the set of x-coordinates: Combine all the [tex]\(x\)[/tex]-values into a set.
[tex]\[
\{3, 6, -1, 5, -4\}
\][/tex]
3. Sort the x-coordinates: Arrange the elements of the set in ascending order for clarity.
[tex]\[
\{-4, -1, 3, 5, 6\}
\][/tex]
4. Identify the correct choice: Compare our sorted set of [tex]\(x\)[/tex]-values with the provided multiple choice options to determine the correct domain.
[tex]\[
\{x \mid x=-4,-1,3,5,6\}
\][/tex]
Given these steps, the domain of the function [tex]\(\{(3,-2), (6,1), (-1,4), (5,9), (-4,0)\}\)[/tex] is:
[tex]\[
\{x \mid x=-4,-1,3,5,6\}
\][/tex]
Therefore, the correct choice is:
[tex]\[
\{x \mid x=-4,-1,3,5,6\}
\][/tex]
This corresponds to the first multiple choice option:
[tex]\[
1
\][/tex]
