Question
What are the domain and range of each relation?
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Points plotted on a coordinate plane. The horizontal x-axis ranges from negative 5 to 5 in increments of 1. The vertical y-axis ranges from negative 5 to 5 in increments of 1. Five points are plotted. Begin ordered pair negative 3 comma 1 end ordered pair. Begin ordered pair negative 1 comma negative 1 end ordered pair. Begin ordered pair 0 comma 0 end ordered pair. Begin ordered pair 3 comma 2 end ordered pair. Begin ordered pair 3 comma 3 end ordered pair.
A relation mapping diagram. Element x contains negative 2, 0, 2, and 4. Element y contains negative 3, negative 1, and 0. Negative 2 maps to negative 3 and negative 1. Zero maps to 0. Two maps to 0. Four maps to negative 3.
Drag the answer into the box to match each relation.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Points plotted on a coordinate plane. The horizontal x-axis ranges from negative 5 to 5 in increments of 1. The vertical y-axis ranges from negative 5 to 5 in increments of 1. Five points are plotted. Begin ordered pair negative 3 comma 1 end ordered pair. Begin ordered pair negative 1 comma negative 1 end ordered pair. Begin ordered pair 0 comma 0 end ordered pair. Begin ordered pair 3 comma 2 end ordered pair. Begin ordered pair 3 comma 3 end ordered pair.
A relation mapping diagram. Element x contains negative 2, 0, 2, and 4. Element y contains negative 3, negative 1, and 0. Negative 2 maps to negative 3 and negative 1. Zero maps to 0. Two maps to 0. Four maps to negative 3.
Answers
GPT-4o mini
To determine the domain and range of the two given relations, we analyze the given points and mappings.
### Relation 1: Coordinate Plane Points
The points plotted on the coordinate plane are:
1. (-3, 1)
2. (-1, -1)
3. (0, 0)
4. (3, 2)
5. (3, 3)
**Domain:**
The domain is the set of all x-values:
- The x-values are: -3, -1, 0, 3, 3
- Removing duplicates, the domain is: **{-3, -1, 0, 3}**
**Range:**
The range is the set of all y-values:
- The y-values are: 1, -1, 0, 2, 3
- The range is: **{-1, 0, 1, 2, 3}**
### Relation 2: Mapping Diagram
The elements are:
- x: {-2, 0, 2, 4}
- y: {-3, -1, 0}
And the mappings are:
- -2 maps to -3 and -1
- 0 maps to 0
- 2 maps to 0
- 4 maps to -3
**Domain:**
The domain consists of all x-values that are mapped:
- The domain is: **{-2, 0, 2, 4}**
**Range:**
The range consists of all y-values that have at least one corresponding x-value:
- The y-values that are mapped to are: -3, -1, 0
- The range is: **{-3, -1, 0}**
### Summary
1. **First Relation (pointed points):**
- Domain: **{-3, -1, 0, 3}**
- Range: **{-1, 0, 1, 2, 3}**
2. **Second Relation (mapping diagram):**
- Domain: **{-2, 0, 2, 4}**
- Range: **{-3, -1, 0}**
### Relation 1: Coordinate Plane Points
The points plotted on the coordinate plane are:
1. (-3, 1)
2. (-1, -1)
3. (0, 0)
4. (3, 2)
5. (3, 3)
**Domain:**
The domain is the set of all x-values:
- The x-values are: -3, -1, 0, 3, 3
- Removing duplicates, the domain is: **{-3, -1, 0, 3}**
**Range:**
The range is the set of all y-values:
- The y-values are: 1, -1, 0, 2, 3
- The range is: **{-1, 0, 1, 2, 3}**
### Relation 2: Mapping Diagram
The elements are:
- x: {-2, 0, 2, 4}
- y: {-3, -1, 0}
And the mappings are:
- -2 maps to -3 and -1
- 0 maps to 0
- 2 maps to 0
- 4 maps to -3
**Domain:**
The domain consists of all x-values that are mapped:
- The domain is: **{-2, 0, 2, 4}**
**Range:**
The range consists of all y-values that have at least one corresponding x-value:
- The y-values that are mapped to are: -3, -1, 0
- The range is: **{-3, -1, 0}**
### Summary
1. **First Relation (pointed points):**
- Domain: **{-3, -1, 0, 3}**
- Range: **{-1, 0, 1, 2, 3}**
2. **Second Relation (mapping diagram):**
- Domain: **{-2, 0, 2, 4}**
- Range: **{-3, -1, 0}**