Question

determine all intervals on which the graph of ( f ) is decreasing.
answer attempt 1 out of 2
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Explanation:

Step1: Identify decreasing intervals

A function is decreasing when its graph moves downward as we move from left to right along the x-axis.

1. First interval: From $x = -7$ to $x = 0$, the graph falls from the peak to the lowest point.
2. Second interval: From $x = 4$ to $+\infty$, the graph falls from its second peak toward negative infinity.

Step2: Write interval notation

Use open parentheses because the endpoints at $x=-7$, $x=0$, and $x=4$ are the points where the function stops decreasing (they are local extrema, so the function is not decreasing at those exact points).

Answer:

$(-7, 0) \cup (4, \infty)$