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:

Sucking Reflex

An automatic response in which an infant sucks on anything placed in their mouth.

Reflex

An involuntary and nearly instantaneous movement in response to a stimulus, without conscious thought or deliberation.

Obtain Food

The process of acquiring foodstuffs for consumption, through various means like purchasing, farming, or hunting.

Grasping Reflex

An involuntary movement or response wherein an infant closes their fingers around an object placed in their hand.