Write the Word or Phrase That Best Completes Each Statement $$f ( x ) = x ^ { 3 } - 0.4 x ^ { 2 } - 2.5861 x + 3.0912$$

question 237

Essay

Write the word or phrase that best completes each statement or answers the question.
Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.
(b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.
- $$f ( x ) = x ^ { 3 } - 0.4 x ^ { 2 } - 2.5861 x + 3.0912$$

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Definitions:

Parasympathetic

Part of the autonomic nervous system responsible for rest and digestion, helping the body to conserve energy and replenish its resources.

Autonomic Nervous System

The part of the nervous system responsible for control of the bodily functions not consciously directed, such as breathing, the heartbeat, and digestive processes.

Hormones

Hormones are chemical messengers produced by the endocrine system that regulate various physiological processes and behaviors in the body.

Endocrine Glands

Glands of the endocrine system that release hormones directly into the blood to regulate body functions.