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=1.5 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 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 and a relative minimum at x=0.555.

Answer 1

Based on the description of the S-shaped curve you provided, here’s an analysis of the options:

• A relative maximum occurs at a point where the function value is higher than nearby points.
• A relative minimum occurs at a point where the function value is lower than nearby points.

Since I cannot see the image, I can guide you on how to identify the key points:

1. Check the curve to find peaks (maximums) and valleys (minimums).
2. Identify the x-values where these occur.

Given the responses:

1. Relative minimum at x=-1 and relative maximum at x=0.555.
2. Relative maximum at x=1.5 and relative minimum at x=-2.
3. Relative maximum at x=-1 and no relative minimum.
4. Relative maximum at x=-1 and a relative minimum at x=0.555.

If your curve has a clear peak at x=-1 and a trough at approximately x=0.555, then the first option is correct. But if the peak is at x=1.5 and the trough is at x=-2, the second option is correct.

To determine which of these statements is most accurate, locate the maximum and minimum points on your graph and select the response that matches those findings.