find the intervals on which the function is increasing, decreasing, or constant.
(-7,2)(-6,2)(-5,2)(-4,2)(-3,2)(-2,2)(-1,2)(1,3)(3,4)(5,5)
Just check the slope on each interval.
increasing when slope > 0
constant when slope = 0
decreasing when slope < 0
Looks like it's constant at 2 for x in (-7,-1)
After that, it's increasing with slope = 1/2
To determine the intervals on which a function is increasing, decreasing, or constant, we need to look at the behavior of the function between each pair of consecutive values given.
Let's analyze each interval:
1. (-7,2): Since the function is constant between -7 and 2, it is neither increasing nor decreasing in this interval.
2. (-6,2): Similar to the previous interval, the function is constant between -6 and 2.
3. (-5,2): The function remains constant in this interval as well.
4. (-4,2): Once again, the function is constant between -4 and 2.
5. (-3,2): The function is still constant between -3 and 2.
6. (-2,2): The function remains constant in this interval.
7. (-1,2): The function is still constant between -1 and 2.
8. (1,3): Finally, the function increases from 1 to 3, so it is increasing in this interval.
9. (3,4): The function also increases from 3 to 4, so it is increasing in this interval.
10. (5,5): Since there is only one value given in this interval, the function is constant.
In summary, the function is increasing in the intervals (1,3) and (3,4). It is constant in all other intervals.
To determine the intervals on which the function is increasing, decreasing, or constant, we need to look at the sign of the first derivative.
Let's denote the function as f(x).
1. Interval (-7, -6):
In this interval, f(x) is decreasing since the y-values decrease as x increases.
2. Interval (-6, -5):
In this interval, f(x) is constant since the y-values remain the same.
3. Interval (-5, -4):
In this interval, f(x) is constant since the y-values remain the same.
4. Interval (-4, -3):
In this interval, f(x) is constant since the y-values remain the same.
5. Interval (-3, -2):
In this interval, f(x) is constant since the y-values remain the same.
6. Interval (-2, -1):
In this interval, f(x) is constant since the y-values remain the same.
7. Interval (-1, 1):
In this interval, f(x) is increasing since the y-values increase as x increases.
8. Interval (1, 3):
In this interval, f(x) is increasing since the y-values increase as x increases.
9. Interval (3, 5):
In this interval, f(x) is increasing since the y-values increase as x increases.
10. Interval (5, 5):
In this interval, f(x) is constant since the y-values remain the same.
Therefore, the intervals on which the function is increasing are (-1, 1), (1, 3), and (3, 5), while the intervals where it is constant are (-6, -5), (-5, -4), (-4, -3), (-3, -2), (-2, -1), and (5, 5). The interval (-7, -6) is where the function is decreasing.