Question

the graph to the right shows the heart rate of a person watching a short romantic film, where x represents time in minutes, and y represents heart rate in beats per minute. answer the following questions.

a. from 3 through 15 minutes
b. from 1 through 3 minutes and from 9 through 11 minutes
c. from 3 through 9 minutes and from 11 through 15 minutes
d. from 1 through 11 minutes

(c) how many turning points (from increasing to decreasing or from decreasing to increasing) occurred for the persons heart rate during the 15 minute film?

(d) suppose that a polynomial function is used to model the data displayed by the graph. what is the degree of the polynomial function of best fit? (use the number of turning points to determine the degree.)

Explanation:

Identify decreasing intervals

Using the Decreasing Intervals and Increasing Intervals knowledge points

• The graph goes down from \(x = 3\) to \(x = 9\).
• The graph goes down from \(x = 11\) to \(x = 15\).
• Thus, the decreasing intervals are from 3 through 9 minutes and from 11 through 15 minutes.

Count the turning points

Using the Turning Points knowledge point

• Peak at \(x = 3\) (increasing to decreasing).
• Valley at \(x = 9\) (decreasing to increasing).
• Peak at \(x = 11\) (increasing to decreasing).
• Total turning points = 3.

Determine the polynomial degree

Using the Degree of Polynomial knowledge point

• A polynomial of degree \(n\) has at most \(n - 1\) turning points.
• The minimum degree for a polynomial with \(k\) turning points is \(n = k + 1\).
• Given \(k = 3\) turning points:

$$ n = 3 + 1 = 4 $$

Answer:

Question 1

• A. from 3 through 15 minutes
• B. from 1 through 3 minutes and from 9 through 11 minutes
• C. from 3 through 9 minutes and from 11 through 15 minutes (Correct answer)
• D. from 1 through 11 minutes

Question 2

The number of turning points is <blank>3</blank>.

Question 3

The degree of the polynomial function of best fit is <blank>4</blank>.