To solve the problem of finding the domain and range of the given set of points, let's go through the solution step by step.
Given set of points:
[tex]\[
\{ (3, -2), (-3, -2), (1, 4), (-6, 5), (1, 3), (-20, 7) \}
\][/tex]
Step 1: Find the Domain
The domain consists of all the x-coordinates from the given set of points.
- From the point (3, -2), the x-coordinate is 3.
- From the point (-3, -2), the x-coordinate is -3.
- From the point (1, 4), the x-coordinate is 1.
- From the point (-6, 5), the x-coordinate is -6.
- From the point (1, 3), the x-coordinate is 1. (Note: This x-coordinate was already listed, so we don't include it again.)
- From the point (-20, 7), the x-coordinate is -20.
So, the domain is the set of unique x-coordinates:
[tex]\[
\{ 3, -3, 1, -6, -20 \}
\][/tex]
Step 2: Find the Range
The range consists of all the y-coordinates from the given set of points.
- From the point (3, -2), the y-coordinate is -2.
- From the point (-3, -2), the y-coordinate is -2. (Note: This y-coordinate was already listed, so we don't include it again.)
- From the point (1, 4), the y-coordinate is 4.
- From the point (-6, 5), the y-coordinate is 5.
- From the point (1, 3), the y-coordinate is 3.
- From the point (-20, 7), the y-coordinate is 7.
So, the range is the set of unique y-coordinates:
[tex]\[
\{ -2, 4, 5, 3, 7 \}
\][/tex]
Therefore, the domain and range of the given set of points are:
- Domain: [tex]\(\{ 3, -3, 1, -6, -20 \} \)[/tex]
- Range: [tex]\(\{ -2, 4, 5, 3, 7 \} \)[/tex]
