Question

analyze the graph and select all properties that apply to the polynomial function.
maximum: (-6.29,11.10) and (-1.98,30.01)
positive: (-6.29,-4.49) and (-5,-4)
maximum: all real numbers
positive: (-7,-5) and (-4,-1)

Explanation:

1. Maxima Identification: The graph has two peaks (local maxima) at the labeled points (-6.29, 11.10) and (-1.98, 30.01). A polynomial with this shape cannot have a maximum of all real numbers, as its ends go to negative infinity.
2. Positive Interval Identification: The graph is above the x-axis (positive) between its leftmost x-intercept (-7, 0) and the next x-intercept (-5, 0), and between the x-intercept (-4, 0) and the rightmost x-intercept (-1, 0). This corresponds to the intervals (-7,-5) and (-4,-1). The other positive interval option lists incorrect, non-intercept bounds.

Answer:

Maximum: (-6.29,11.10) and (-1.98,30.01)
Positive: (-7,-5) and (-4,-1)