Write the Word or Phrase That Best Completes Each Statement $$f ( x ) = ( x - 3 ) ( x - 1 ) ( x + 2 )$$

question 38

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.
- $$f ( x ) = ( x - 3 ) ( x - 1 ) ( x + 2 )$$

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Definitions:

Trichiasis

A condition where eyelashes grow abnormally and irritate the eyes.

Xerophthalmia

A medical condition characterized by dry eyes due to a lack of vitamin A, which can lead to vision problems.

Orthoptics

A branch of ophthalmology dealing with the diagnosis and treatment of defective vision and the management of eye movement disorders.

Lens

A piece of glass or other transparent material with curved sides for concentrating or dispersing light rays, used in glasses and cameras.