To analyze the relative maximum and minimum of the polynomial function \( h(x) \) based on the provided points, we can look at the given points in terms of their \( y \)-values at each corresponding \( x \):
- Point (-1, 4): This is the highest value among the given points, indicating a relative maximum.
- Point (0, 0): This point is lower than the value at (-1, 4) and has a higher value at (0.5, 1.5), indicating it's a minimum point.
- Point (0.5, 1.5): This point is lower than 4 but higher than 0.
- Point (1, 0): This point is the same as (0, 0) but is part of a decrease as \( x \) values move from (0.5, 1.5) to (1, 0).
Given this analysis, we can conclude:
- There is a relative maximum at \( x = -1 \) with \( h(-1) = 4 \).
- There is a relative minimum at \( x = 0 \) with \( h(0) = 0 \).
Examining the response options provided:
- The best fit is: "There is a relative maximum at \( x = -1 \) and a relative minimum at \( x = 0 \)."
However, none of the responses directly correspond with our findings. It appears the analysis missed some values. Typically, we would need the function's derivative and potentially test intervals between points to confirm. Nevertheless, based on the graph points given and their respective secondary values, it would need additional context to see if the specific (0.555) minimum holds valid evidence.
Thus:
- There is an absolute maximum at x = -1.
- The closest and accurate interpretation of value drops support a relative minimum at x = 0 or between intervals as the nature of ranges adjust furthermore.
Please review the provided graphical points as the polynomial nature and its behavior might yield distinct answers or confirm in conditions presented.