To find the range of the given function, we need to examine the y-values corresponding to each coordinate pair [tex]\((x, y)\)[/tex] provided.
The given coordinates are:
- [tex]\((-5, 9)\)[/tex]
- [tex]\((1, 0)\)[/tex]
- [tex]\((4, -7)\)[/tex]
- [tex]\((6, -1)\)[/tex]
Step-by-step, let's list the y-values:
- For coordinate [tex]\((-5, 9)\)[/tex], the y-value is [tex]\(9\)[/tex].
- For coordinate [tex]\((1, 0)\)[/tex], the y-value is [tex]\(0\)[/tex].
- For coordinate [tex]\((4, -7)\)[/tex], the y-value is [tex]\(-7\)[/tex].
- For coordinate [tex]\((6, -1)\)[/tex], the y-value is [tex]\(-1\)[/tex].
Now, we collate all the y-values:
[tex]\[ 9, 0, -7, -1 \][/tex]
After listing these y-values, we remove any duplicates (though none exist in this case) and sort them in ascending order:
[tex]\[ -7, -1, 0, 9 \][/tex]
Thus, the range of the function, which is the set of all distinct y-values from the given points, is:
[tex]\[ \{ y \mid y = -7, -1, 0, 9 \} \][/tex]
Therefore, the correct option for the range of the given function is:
[tex]\[ \{ y \mid y = -7, -1, 0, 9 \} \][/tex]
