Use the image to answer the question.

Question

A horizontal S-shaped curve is plotted on a coordinate plane with both axes ranging from negative 5 to 5 in unit increments.

Which of the following most accurately identifies the relative maximum and minimum of the polynomial function h(x)?

(1 point)
Responses

There is a relative minimum at x=−1 and a relative maximum at x=0.555.
There is a relative minimum at x equals negative 1 and a relative maximum at x equals 0.555 .

There is a relative maximum at x=−1 and no relative minimum.
There is a relative maximum at x equals negative 1 and no relative minimum.

There is a relative maximum at x=1.5 and a relative minimum at x=−2.
There is a relative maximum at x equals 1.5 and a relative minimum at x equals negative 2 .

There is a relative maximum at x=−1 and a relative minimum at x=0.555.

Answer 1

Based on the description of the S-shaped curve and the various options given, we can deduce the following about the relative maximum and minimum points of the polynomial function h(x):

• A relative minimum occurs where the curve reaches a low point before rising again, while a relative maximum is where the curve reaches a high point before falling again.
• Typically, for an S-shaped curve, you'd expect to see at least one maximum and one minimum.

Given your options:

1. There is a relative minimum at x = −1 and a relative maximum at x = 0.555.
2. There is a relative maximum at x = −1 and no relative minimum.
3. There is a relative maximum at x = 1.5 and a relative minimum at x = −2.
4. There is a relative maximum at x = −1 and a relative minimum at x = 0.555.

From these considerations, the correct identification of relative extrema would depend on the exact behavior of the curve at the specified x-values. However, without visual confirmation from the image, the most plausible option for an S-shaped curve would be:

There is a relative minimum at x = −1 and a relative maximum at x = 0.555.

This option reflects typical behavior of an S-shaped curve.