Let's find the range of the given function with the set of points:
[tex]\[
\{(-2,0),(-4,-3),(2,-9),(0,5),(-5,7)\}
\][/tex]
The range of a function consists of all possible values that the dependent variable \( y \) can take. To find these values, we'll look at the \( y \)-coordinates of the provided points.
First, we list all the given points:
1. \((-2, 0)\)
2. \((-4, -3)\)
3. \((2, -9)\)
4. \((0, 5)\)
5. \((-5, 7)\)
Next, extract all the \( y \)-coordinates from these points:
- \( y = 0 \)
- \( y = -3 \)
- \( y = -9 \)
- \( y = 5 \)
- \( y = 7 \)
Now, let's arrange these \( y \)-values in ascending order and remove any duplicates:
[tex]\[
\{ -9, -3, 0, 5, 7 \}
\][/tex]
Therefore, the range of the given function is:
[tex]\[
\{ y \mid y = -9, -3, 0, 5, 7 \}
\][/tex]
Among the provided options, the correct one describing the range of the function is:
[tex]\[
\{ y \mid y = -9, -3, 0, 5, 7 \}
\][/tex]
So, the correct answer is:
[tex]\[
\{ y \mid y = -9, -3, 0, 5, 7 \}
\][/tex]
