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:

Emancipation Requirement

Specific conditions or laws that mandate the freeing of slaves or enslaved individuals.

Smaller States

Countries or states with relatively small territorial size or population compared to larger nations.

Constitutional Convention

The gathering in 1787 where the Constitution of the United States was framed and drafted by delegates representing the states.