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.

(e) for the model in part (d), should the leading coefficient of the polynomial function be positive or negative? why?
a. positive because the graph falls to the left and rises to the right
b. positive because the graph falls to the left and falls to the right
c. negative because the graph rises to the left and falls to the right
d. negative because the graph falls to the left and falls to the right

(f) use the graph to estimate the persons maximum heart rate during the 15 minute film.
bpm

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.

(e) for the model in part (d), should the leading coefficient of the polynomial function be positive or negative? why?
a. positive because the graph falls to the left and rises to the right
b. positive because the graph falls to the left and falls to the right
c. negative because the graph rises to the left and falls to the right
d. negative because the graph falls to the left and falls to the right

(f) use the graph to estimate the persons maximum heart rate during the 15 minute film.
  bpm

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Leading Coefficient Test", "End Behavior of Polynomials", "Graph Interpretation" ], "new_concepts": [], "current_concepts": [ "Leading Coefficient Test", "End Behavior of Polynomials", "Graph Interpretation" ] } ## Analyze end behavior of the polynomial model Using the *Leading Coefficient Test* and *End Behavior of Polynomials* knowledge points $$ \begin{aligned} &\text{As } x \to -\infty, \quad y \to -\infty \quad (\text{falls to the left})\ &\text{As } x \to \infty, \quad y \to -\infty \quad (\text{falls to the right})\ &\text{Since both ends fall, the leading coefficient must be negative.} \end{aligned} $$ ## Estimate the maximum heart rate from the graph Using the *Graph Interpretation* knowledge point $$ \begin{aligned} &\text{Peak of the curve occurs near } x = 3.\ &y\text{-value at this peak is just below } 70\text{ bpm.}\ &\text{Estimated maximum value } \approx 69\text{ bpm.} \end{aligned} $$ ## Question (e) A. positive because the graph falls to the left and rises to the right

B. positive because the graph falls to the left and falls to the right

C. negative because the graph rises to the left and falls to the right

D. negative because the graph falls to the left and falls to the right ## Question (f) 69 bpm { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "End Behavior of Polynomials" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Analyze end behavior of the polynomial model

Estimate the maximum heart rate from the graph

Answer:

Question (e)

Question (f)