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

question 72

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.
- $$f ( x ) = x ^ { 2 } ( x + 3 )$$

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Definitions:

Company Retirement

Often related to the benefits or pension schemes planned for employees after they retire from a company, differing from mandatory retirement policies.

Savings Programs

Financial plans or accounts that encourage saving by offering interest or other benefits.

Neoclassical Models

Economic models based on the principles of neoclassical economics that emphasize rational behavior, supply and demand equilibrium, and the efficiency of markets.

Behavioral Economics

A field of economics that studies how psychological, cognitive, emotional, cultural, and social factors affect the economic decisions of individuals and institutions.