Question
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each equation of the piecewise function represented in the graph to its corresponding piece of the domain.
Graph shows a piecewise function plotted on a coordinate plane. It has 4 segments. Segment 1 has closed dots at (0, 1) and (1, 1). Segment 2 has closed dots at (1, 1) and (2, 2). Segment 3 has closed dots at (2, 3) and (3, 3).
f(x) = x
f(x) = 3
f(x) = 2
f(x) = 4
f(x) = 1
f(x) = -x
f(x) = 2 − x
Domain
Function Equation
1 ≤ x ≤ 2
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0 < x ≤ 1
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3 < x ≤ 4
arrowRight
2 < x ≤ 3
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Match each equation of the piecewise function represented in the graph to its corresponding piece of the domain.
Graph shows a piecewise function plotted on a coordinate plane. It has 4 segments. Segment 1 has closed dots at (0, 1) and (1, 1). Segment 2 has closed dots at (1, 1) and (2, 2). Segment 3 has closed dots at (2, 3) and (3, 3).
f(x) = x
f(x) = 3
f(x) = 2
f(x) = 4
f(x) = 1
f(x) = -x
f(x) = 2 − x
Domain
Function Equation
1 ≤ x ≤ 2
arrowRight
0 < x ≤ 1
arrowRight
3 < x ≤ 4
arrowRight
2 < x ≤ 3
arrowRight
Answers
GPT-4o mini
To match the equations of the piecewise function to their corresponding segments of the domain based on the described graph, we analyze each segment:
1. **Segment 1**: It goes from (0, 1) to (1, 1). This is a horizontal line at \(y = 1\) for the interval \(0 < x ≤ 1\).
- **Equation**: \(f(x) = 1\)
- **Domain**: \(0 < x ≤ 1\)
2. **Segment 2**: It goes from (1, 1) to (2, 2). Here, the function is rising linearly from \(y = 1\) to \(y = 2\), which is described by \(f(x) = x\).
- **Equation**: \(f(x) = x\)
- **Domain**: \(1 ≤ x ≤ 2\)
3. **Segment 3**: It goes from (2, 3) to (3, 3). This is another horizontal line at \(y = 3\) for the interval \(2 < x ≤ 3\).
- **Equation**: \(f(x) = 3\)
- **Domain**: \(2 < x ≤ 3\)
4. **Segment 4**: The description does not mention a fourth segment thoroughly, but if it were present, it would be for \(3 < x ≤ 4\) and could be represented by a different linear function, but we can’t assign any equation from the list for this segment.
So, the matches would be:
1. **Domain**: \(0 < x ≤ 1\) → **Function Equation**: \(f(x) = 1\)
2. **Domain**: \(1 ≤ x ≤ 2\) → **Function Equation**: \(f(x) = x\)
3. **Domain**: \(2 < x ≤ 3\) → **Function Equation**: \(f(x) = 3\)
As such, the arrangements are:
- \(1 ≤ x ≤ 2\) → \(f(x) = x\)
- \(0 < x ≤ 1\) → \(f(x) = 1\)
- \(2 < x ≤ 3\) → \(f(x) = 3\)
The unused domains and equations do not apply to the segments you provided.
1. **Segment 1**: It goes from (0, 1) to (1, 1). This is a horizontal line at \(y = 1\) for the interval \(0 < x ≤ 1\).
- **Equation**: \(f(x) = 1\)
- **Domain**: \(0 < x ≤ 1\)
2. **Segment 2**: It goes from (1, 1) to (2, 2). Here, the function is rising linearly from \(y = 1\) to \(y = 2\), which is described by \(f(x) = x\).
- **Equation**: \(f(x) = x\)
- **Domain**: \(1 ≤ x ≤ 2\)
3. **Segment 3**: It goes from (2, 3) to (3, 3). This is another horizontal line at \(y = 3\) for the interval \(2 < x ≤ 3\).
- **Equation**: \(f(x) = 3\)
- **Domain**: \(2 < x ≤ 3\)
4. **Segment 4**: The description does not mention a fourth segment thoroughly, but if it were present, it would be for \(3 < x ≤ 4\) and could be represented by a different linear function, but we can’t assign any equation from the list for this segment.
So, the matches would be:
1. **Domain**: \(0 < x ≤ 1\) → **Function Equation**: \(f(x) = 1\)
2. **Domain**: \(1 ≤ x ≤ 2\) → **Function Equation**: \(f(x) = x\)
3. **Domain**: \(2 < x ≤ 3\) → **Function Equation**: \(f(x) = 3\)
As such, the arrangements are:
- \(1 ≤ x ≤ 2\) → \(f(x) = x\)
- \(0 < x ≤ 1\) → \(f(x) = 1\)
- \(2 < x ≤ 3\) → \(f(x) = 3\)
The unused domains and equations do not apply to the segments you provided.