Question
A graph on a coordinate plane shows a function with one line segment and one curved segment that are disjoint.The coordinate plane has an x-axis range of negative 10 to 10 and a y-axis range of negative 10 to 10. There is a line segment connecting an open point at left-parenthesis negative 6 comma negative 3 right-parenthesis and a closed point at left-parenthesis 2 comma 2 right-parenthesis. A curve connects an open point at left-parenthesis 1 comma 7 right-parenthesis and a closed point at left-parenthesis 5 comma 3 right-parenthesis.
Question
Use the graph of the function to answer the question.
Find the domain and range of the function shown in the graph. Write the domain and range using interval notation.
(1 point)
Responses
domain: left-bracket negative 3 comma 2 right-parenthesis union left-parenthesis 3 comma 7 right-bracket
range: left-bracket negative 6 comma negative 1 right-parenthesis union left-bracket 1 comma 5 right-parenthesis
domain: Image with alt text: left-bracket negative 3 comma 2 right-parenthesis union left-parenthesis 3 comma 7 right-bracket range: Image with alt text: left-bracket negative 6 comma negative 1 right-parenthesis union left-bracket 1 comma 5 right-parenthesis
domain: left-parenthesis negative 6 comma negative 1 right-bracket union left-parenthesis 1 comma 5 right-bracket
range: left-parenthesis negative 3 comma 2 right-bracket union left-bracket 3 comma 7 right-parenthesis
domain: Image with alt text: left-parenthesis negative 6 comma negative 1 right-bracket union left-parenthesis 1 comma 5 right-bracket range: Image with alt text: left-parenthesis negative 3 comma 2 right-bracket union left-bracket 3 comma 7 right-parenthesis
domain: left-parenthesis negative 3 comma 2 right-bracket union left-bracket 3 comma 7 right-parenthesis
range: left-parenthesis negative 6 comma negative 1 right-bracket union left-parenthesis 1 comma 5 right-bracket
domain: Image with alt text: left-parenthesis negative 3 comma 2 right-bracket union left-bracket 3 comma 7 right-parenthesis range: Image with alt text: left-parenthesis negative 6 comma negative 1 right-bracket union left-parenthesis 1 comma 5 right-bracket
domain: left-bracket negative 6 comma negative 1 right-parenthesis union left-bracket 1 comma 5 right-parenthesis
range: left-bracket negative 3 comma 2 right-parenthesis union left-parenthesis 3 comma 7 right-bracket
domain: Image with alt text: left-bracket negative 6 comma negative 1 right-parenthesis union left-bracket 1 comma 5 right-parenthesis range: Image with alt text: left-bracket negative 3 comma 2 right-parenthesis union left-parenthesis 3 comma 7 right-bracket
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Question
Use the graph of the function to answer the question.
Find the domain and range of the function shown in the graph. Write the domain and range using interval notation.
(1 point)
Responses
domain: left-bracket negative 3 comma 2 right-parenthesis union left-parenthesis 3 comma 7 right-bracket
range: left-bracket negative 6 comma negative 1 right-parenthesis union left-bracket 1 comma 5 right-parenthesis
domain: Image with alt text: left-bracket negative 3 comma 2 right-parenthesis union left-parenthesis 3 comma 7 right-bracket range: Image with alt text: left-bracket negative 6 comma negative 1 right-parenthesis union left-bracket 1 comma 5 right-parenthesis
domain: left-parenthesis negative 6 comma negative 1 right-bracket union left-parenthesis 1 comma 5 right-bracket
range: left-parenthesis negative 3 comma 2 right-bracket union left-bracket 3 comma 7 right-parenthesis
domain: Image with alt text: left-parenthesis negative 6 comma negative 1 right-bracket union left-parenthesis 1 comma 5 right-bracket range: Image with alt text: left-parenthesis negative 3 comma 2 right-bracket union left-bracket 3 comma 7 right-parenthesis
domain: left-parenthesis negative 3 comma 2 right-bracket union left-bracket 3 comma 7 right-parenthesis
range: left-parenthesis negative 6 comma negative 1 right-bracket union left-parenthesis 1 comma 5 right-bracket
domain: Image with alt text: left-parenthesis negative 3 comma 2 right-bracket union left-bracket 3 comma 7 right-parenthesis range: Image with alt text: left-parenthesis negative 6 comma negative 1 right-bracket union left-parenthesis 1 comma 5 right-bracket
domain: left-bracket negative 6 comma negative 1 right-parenthesis union left-bracket 1 comma 5 right-parenthesis
range: left-bracket negative 3 comma 2 right-parenthesis union left-parenthesis 3 comma 7 right-bracket
domain: Image with alt text: left-bracket negative 6 comma negative 1 right-parenthesis union left-bracket 1 comma 5 right-parenthesis range: Image with alt text: left-bracket negative 3 comma 2 right-parenthesis union left-parenthesis 3 comma 7 right-bracket
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Answers
GPT-4o mini
To find the domain and range of the function described, we can analyze the given segments:
1. **Line Segment**: This connects the open point at \((-6, -3)\) to the closed point at \((2, 2)\). The x-values for this segment range from \(-6\) to \(2\) (not including \(-6\) and including \(2\)). Therefore, the domain contribution from this segment is:
\[
(-6, 2]
\]
2. **Curved Segment**: This connects the open point at \((1, 7)\) to the closed point at \((5, 3)\). The x-values for this curve range from \(1\) to \(5\) (not including \(1\) and including \(5\)). Thus, the domain contribution from this segment is:
\[
(1, 5]
\]
Now, since there is no overlap between the intervals of the two segments, we can combine them to write the overall domain as:
\[
(-6, 2] \cup (1, 5]
\]
Next, we examine the range of the function defined by these segments.
1. For the **Line Segment** from the point \((-6, -3)\) to \((2, 2)\), the y-values start from \(-3\) (not included) to \(2\) (included), giving us:
\[
(-3, 2]
\]
2. For the **Curved Segment** from the point \((1, 7)\) to \((5, 3)\), the y-values range from \(7\) (not included) to \(3\) (included), but since the y-values cannot go below \(3\) in this segment, the range contribution would be from \(3\) to \(7\):
\[
(3, 7)
\]
Again, there is no overlap, so we combine the ranges:
\[
(-3, 2] \cup (3, 7)
\]
Combining both results, we conclude:
- **Domain**: \((-6, 2] \cup (1, 5]\)
- **Range**: \((-3, 2] \cup (3, 7)\)
So the correct response will be:
- Domain: \((-6, 2] \cup (1, 5]\)
- Range: \((-3, 2] \cup (3, 7)\)
These intervals ensure all values are captured based on the segments described.
1. **Line Segment**: This connects the open point at \((-6, -3)\) to the closed point at \((2, 2)\). The x-values for this segment range from \(-6\) to \(2\) (not including \(-6\) and including \(2\)). Therefore, the domain contribution from this segment is:
\[
(-6, 2]
\]
2. **Curved Segment**: This connects the open point at \((1, 7)\) to the closed point at \((5, 3)\). The x-values for this curve range from \(1\) to \(5\) (not including \(1\) and including \(5\)). Thus, the domain contribution from this segment is:
\[
(1, 5]
\]
Now, since there is no overlap between the intervals of the two segments, we can combine them to write the overall domain as:
\[
(-6, 2] \cup (1, 5]
\]
Next, we examine the range of the function defined by these segments.
1. For the **Line Segment** from the point \((-6, -3)\) to \((2, 2)\), the y-values start from \(-3\) (not included) to \(2\) (included), giving us:
\[
(-3, 2]
\]
2. For the **Curved Segment** from the point \((1, 7)\) to \((5, 3)\), the y-values range from \(7\) (not included) to \(3\) (included), but since the y-values cannot go below \(3\) in this segment, the range contribution would be from \(3\) to \(7\):
\[
(3, 7)
\]
Again, there is no overlap, so we combine the ranges:
\[
(-3, 2] \cup (3, 7)
\]
Combining both results, we conclude:
- **Domain**: \((-6, 2] \cup (1, 5]\)
- **Range**: \((-3, 2] \cup (3, 7)\)
So the correct response will be:
- Domain: \((-6, 2] \cup (1, 5]\)
- Range: \((-3, 2] \cup (3, 7)\)
These intervals ensure all values are captured based on the segments described.