To determine whether a function is increasing, decreasing, or constant over specific intervals, we would typically analyze the slope of the graph in each interval:
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For the interval \( 1 < x < 2 \):
- If the graph is rising as \( x \) moves from 1 to 2, the function is increasing.
- If the graph is falling during this interval, the function is decreasing.
- If the graph is flat (horizontal), the function is constant.
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For the interval \( 2 < x < 5 \):
- Similarly, check if the graph rises, falls, or remains flat in this interval.
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For the interval \( 5 < x < 7 \):
- Again, observe if the graph is increasing, decreasing, or constant.
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For the interval \( x > 7 \):
- Determine whether the graph continues to rise, fall, or stay flat after 7.
You would need to visually inspect the graph in question for these intervals.
- If you have the graph available, look at the slopes in each of the specified ranges.
- If the graph was provided, I could give more specific guidance.
For each interval, you should summarize your findings with one of the following statements:
- "The function is increasing."
- "The function is decreasing."
- "The function is constant."
If you can provide details about the graph or its shape in these intervals, I can help you with more specific answers!