Question
The graph shows yyy as a function of xxx.
For each interval in the table, indicate whether the function is increasing, decreasing, or neither increasing nor decreasing over the interval.
Increasing
Decreasing
Neither Increasing or Decreasing
−
7
<
x
<
−
3
−7<x<−3
−
3
<
x
<
−
1
−3<x<−1
−
1
<
x
<
1
−1<x<1
1
<
x
<
3
1<x<3
3
<
x
<
5
3<x<5
5
<
x
<
7
5<x<7
For each interval in the table, indicate whether the function is increasing, decreasing, or neither increasing nor decreasing over the interval.
Increasing
Decreasing
Neither Increasing or Decreasing
−
7
<
x
<
−
3
−7<x<−3
−
3
<
x
<
−
1
−3<x<−1
−
1
<
x
<
1
−1<x<1
1
<
x
<
3
1<x<3
3
<
x
<
5
3<x<5
5
<
x
<
7
5<x<7
Answers
Answered by
GPT-4o mini
To determine whether the function is increasing, decreasing, or neither on the specified intervals, we would typically analyze the graph of the function. Since I don't have visibility of the actual graph, I can guide you on how to evaluate each interval based on the behavior of the graph.
1. **Increasing**: The function is increasing on an interval if the y-values (outputs) rise as the x-values (inputs) increase.
2. **Decreasing**: The function is decreasing on an interval if the y-values fall as the x-values increase.
3. **Neither Increasing nor Decreasing**: The function is neither increasing nor decreasing if the y-values remain constant or if they fluctuate without a clear upward or downward trend.
### How to Analyze Each Interval:
- For each specified interval, look at the graph and identify the trend:
- **From -7 to -3**: Does the function rise or fall?
- **From -3 to -1**: Check if the function is moving up or down.
- **From -1 to 1**: Look at the trend within these x-values.
- **From 1 to 3**: Again, evaluate the function's movement.
- **From 3 to 5**: What is the function doing in this interval?
- **From 5 to 7**: Finally, check the trend here.
### Example Responses:
1. For interval \((-7, -3)\): (Increasing/Decreasing/Neither)
2. For interval \((-3, -1)\): (Increasing/Decreasing/Neither)
3. For interval \((-1, 1)\): (Increasing/Decreasing/Neither)
4. For interval \((1, 3)\): (Increasing/Decreasing/Neither)
5. For interval \((3, 5)\): (Increasing/Decreasing/Neither)
6. For interval \((5, 7)\): (Increasing/Decreasing/Neither)
Please refer to the graph you have in front of you and analyze each interval based on the trends you observe.
1. **Increasing**: The function is increasing on an interval if the y-values (outputs) rise as the x-values (inputs) increase.
2. **Decreasing**: The function is decreasing on an interval if the y-values fall as the x-values increase.
3. **Neither Increasing nor Decreasing**: The function is neither increasing nor decreasing if the y-values remain constant or if they fluctuate without a clear upward or downward trend.
### How to Analyze Each Interval:
- For each specified interval, look at the graph and identify the trend:
- **From -7 to -3**: Does the function rise or fall?
- **From -3 to -1**: Check if the function is moving up or down.
- **From -1 to 1**: Look at the trend within these x-values.
- **From 1 to 3**: Again, evaluate the function's movement.
- **From 3 to 5**: What is the function doing in this interval?
- **From 5 to 7**: Finally, check the trend here.
### Example Responses:
1. For interval \((-7, -3)\): (Increasing/Decreasing/Neither)
2. For interval \((-3, -1)\): (Increasing/Decreasing/Neither)
3. For interval \((-1, 1)\): (Increasing/Decreasing/Neither)
4. For interval \((1, 3)\): (Increasing/Decreasing/Neither)
5. For interval \((3, 5)\): (Increasing/Decreasing/Neither)
6. For interval \((5, 7)\): (Increasing/Decreasing/Neither)
Please refer to the graph you have in front of you and analyze each interval based on the trends you observe.