Use the image to answer the question.

Question

A horizontal S-shaped curve is plotted on a coordinate plane with the x-axis ranging from negative 2 to 4 in increments of 0.5 and the y-axis ranging from negative 4 to 4 in increments of 0.5.

Brandon was asked to identify the relative maximum of the polynomial function h(x) . Which answer choice identifies the correct value(s)?

(1 point)
Responses

There is a relative minimum at x=1.
There is a relative minimum at x equals 1 .

There is no relative maximum in this graph.
There is no relative maximum in this graph.

There is a relative maximum at x=0.
There is a relative maximum at x equals 0 .

There is a relative maximum at x=2.

Answer 1

To identify the relative maximum of the polynomial function \( h(x) \) based on the description of an S-shaped curve, look for the peaks of the curve where it changes direction from increasing to decreasing.

From the options, we focus on potential locations for relative maxima:

• If the curve peaks at \( x = 0 \) or \( x = 2 \), those points could be relative maximums.
• If \( x = 1 \) is a point where the curve is at a low point (valley), that indicates a relative minimum.

Given the common characteristics of an S-shaped curve, it likely has relative maximums at the peaks. Assuming you observed the curve carefully, you can deduce whether \( x = 0 \) or \( x = 2 \) is a peak.

With the choices available:

• If the graph shows that the curve has a local peak at \( x = 0 \), the correct answer is: There is a relative maximum at \( x = 0 \).
• If the peak is at \( x = 2 \) instead, then the correct answer is: There is a relative maximum at ( x = 2.*
• If neither x = 0 nor x = 2 are peaks, then the statement says There is no relative maximum in this graph.

If you can confirm visually from the graph, choose the option that matches your observation!