Based on the description of the S-shaped curve, we can identify key features such as relative minima and maxima.
- A relative maximum occurs at a peak point in the curve where the function changes direction from increasing to decreasing.
- A relative minimum occurs at a trough point in the curve where the function changes direction from decreasing to increasing.
Given the options provided:
- For the first option, relative minimum at (0, -2) and relative maximum at (4, 0) doesn't align with typical S-shaped curves, as a max at (4, 0) would imply the function is increasing towards (4, 0) and then is decreasing, which conflicts with the S-shape.
- For the second and third options regarding maxima and minima at points such as (−2, 0) and (0, 4), these also seem inconsistent with the S-shape.
Without the specific visual of the graph, the most common understanding of an S-shaped curve is that it has:
- A relative maximum in the center (higher up) where it turns from increasing to decreasing.
- A relative minimum at the bottom end where it turns from decreasing to increasing.
Thus the one that best matches typical behavior for an S-shape is:
There is a relative maximum at (−2, 0) and a relative minimum at (0, 4).
This aligns with the general expected behavior of polynomial functions modeled in an S-curve format.