Write the Word or Phrase That Best Completes Each Statement $$f ( x ) = x ^ { 2 } \left( x ^ { 2 } - 4 \right) ( x + 4 )$$

question 178

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.
- $$f ( x ) = x ^ { 2 } \left( x ^ { 2 } - 4 \right) ( x + 4 )$$

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Definitions:

Thinking Stops

describes a cessation or significant interruption in the cognitive process, often due to stress, overwhelming information, or mental health issues, preventing effective problem-solving or decision-making.

Vulnerable to Suggestion

A state or condition where an individual is more likely to accept or agree with ideas, proposals, or commands without critical analysis or investigation.

Eyewitness Memory

The ability of a person who has witnessed a crime or event to remember and describe specific details about what they saw.

Preschool-aged Child

Describes children typically between the ages of 3 to 5 years, who are in the developmental stage prior to entering elementary school.