To determine the intervals over which the function is decreasing based on the description of the three branches of the graph, we should analyze each branch accordingly.
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First Branch (as described):
- Domain: This branch covers the interval to the left of -3 (i.e., from negative infinity to -3).
- Behavior: It appears to be increasing as it passes through points such as (-6, 0.333), (-4.5, 0.8), and (-3.5, 2.769).
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Second Branch (around x = -3):
- Domain: This branch covers the interval from just to the right of -3 to 3.
- Behavior: The function decreases as it moves through the points (-2.5, -3.273), (-1, -1.125), (0, -1), and (1, -1.125).
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Third Branch (to the right of x = 3):
- Domain: This branch starts just to the right of 3 and continues to infinity.
- Behavior: The function appears to be increasing since it moves through points like (3.5, 2.769), (4.5, 0.8), and (6, 0.333).
Given this analysis, the function is decreasing in the interval where the second branch operates:
Interval where the function is decreasing: \( \left(-3, 3\right) \)
Thus, the appropriate response based on the provided options is:
left parenthesis 0 comma 3 right parenthesis union left parenthesis 3 comma infinity right parenthesis
However, please note that the correct decreasing interval considering the behavior of the second branch is only \( \left(-3, 3\right) \) (not listed as an option):
- left parenthesis negative infinity comma negative 3 right parenthesis union left parenthesis negative 3 comma 0 right parenthesis would indicate decreasing on both sides of -3, which is not correct.
The intervals provided as answers do not clear up the possible confusion, but the concluding correct interval based on your description of the branches is, importantly, \( (-3, 3) \).
1 answer