A function is graphed on the coordinate plane.The function graphed has 3 branches. The first branch starts just above the x-axis and passes through the approximate points left parenthesis negative 6 comma 0.333 right parenthesis, left parenthesis negative 4.5 comma 0.8 right parenthesis, and left parenthesis negative 3.5 comma 2.769 right parenthesis, approaching but never reaching x equals negative 3. The second branch starts at the bottom of the graph just to the right of x equals negative 3 and passes through the approximate points left parenthesis negative 2.5 comma negative 3.273 right parenthesis, left parenthesis negative 1 comma negative 1.125 right parenthesis, left-parenthesis 0 comma negative 1 right-parenthesis, left parenthesis 1 comma negative 1.125 right parenthesis, and left parenthesis 2.5 comma negative 3.273 right parenthesis, approaching but never reaching x equals 3. The third branch starts just to the right of x equals 3 and passes through the approximate points left parenthesis 3.5 comma 2.769 right parenthesis, left parenthesis 4.5 comma 0.8 right parenthesis, and left parenthesis 6 comma 0.333 right parenthesis, approaching but never reaching the x-axis.

Question

Question
Use the graph to answer the question.
Find the interval(s) over which the function is decreasing.
(1 point)
Responses

left parenthesis negative infinity comma negative 3 right parenthesis
Image with alt text: left parenthesis negative infinity comma negative 3 right parenthesis

left parenthesis 3 comma infinity right parenthesis
Image with alt text: left parenthesis 3 comma infinity right parenthesis

left parenthesis 0 comma 3 right parenthesis union left parenthesis 3 comma infinity right parenthesis
Image with alt text: left parenthesis 0 comma 3 right parenthesis union left parenthesis 3 comma infinity right parenthesis

left parenthesis negative infinity comma negative 3 right parenthesis union left parenthesis negative 3 comma 0 right parenthesis
Image with alt text: left parenthesis negative infinity comma negative 3 right parenthesis union left parenthesis negative 3 comma 0 right parenthesis
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Answer 1

To determine the intervals where the function is decreasing based on the description of its branches:

1. First Branch: This branch starts just above the x-axis, approaches but never reaches \( x = -3 \) from the left, and is increasing as it moves from \( x = -6 \) to \( x = -3 \). Therefore, this branch does not contribute any intervals of decrease.

2. Second Branch: This branch starts right after \( x = -3 \) and continues downwards through \( (-2.5, -3.273), (-1, -1.125), (0, -1), (1, -1.125), (2.5, -3.273) \) as it approaches but never reaches \( x = 3 \). This indicates that this part of the function is decreasing, specifically in the interval \( (-3, 3) \).

3. Third Branch: This branch starts right after \( x = 3 \) and moves upwards through \( (3.5, 2.769), (4.5, 0.8), (6, 0.333) \). Since it is increasing, it does not contribute to the intervals of decrease.

From this analysis, we conclude that the function is decreasing only in the interval \( (-3, 3) \).

Therefore, none of the provided response options fully describe the interval of decrease, but the correct decreasing interval is \( (-3, 3) \). If you are required to choose from the options based on the closest available ones, the best choice would be:

left parenthesis 0 comma 3 right parenthesis union left parenthesis 3 comma infinity right parenthesis

However, note that the accurate interpretation of the decreasing interval should have been just \( (-3, 3) \).