Question

5.6.3 quiz: graphing polynomial functions
question 9 of 10
which point is the best approximation of the relative maximum of the polynomial function graphed below?
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a. (-2.7, 16)
b. (-3.6, 17)
c. (-2.2, 15)
d. (-1.8, 15)

Explanation:

Step1: Understand the concept of relative maximum

A relative maximum of a function is a point where the function changes from increasing to decreasing. On the graph, it is the "peak" of a local rise.

Step2: Analyze the x - coordinate range

Looking at the graph, the x - coordinate of the relative maximum is between - 4 and - 2.

Step3: Analyze the y - coordinate range

The y - coordinate of the relative maximum is around 17.

Step4: Check the options

• Option A: \(x=-2.7\), \(y = 16\). The y - value is lower than what seems appropriate from the graph.
• Option B: \(x=-3.6\) (which is between - 4 and - 2) and \(y = 17\). This matches the approximate position of the relative maximum.
• Option C: \(x=-2.2\), \(y = 15\). The y - value is too low.
• Option D: \(x=-1.8\), \(y = 15\). The x - value is not in the correct range and the y - value is too low.

Answer:

B. \((-3.6,17)\)