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

question 50

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

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Definitions:

Ancestry

The lineage or descent of a person or group, especially regarding family background or ethnicity.

Extermination

The act of completely destroying or eliminating something or someone, often used in the context of genocide or pest control.

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Milk that is recently obtained from an animal, without undergoing processing such as pasteurization or homogenization.

Subspecies

A taxonomic category that ranks below species, used to classify variations within a species that are distinct in form or behavior, but still capable of interbreeding.