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

question 212

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

---

Definitions:

Finite Population Correction Factor

A correction used in sampling to adjust for the effect of sampling without replacement from a finite population.

Subset

A set of elements that are all members of another set, and possibly fewer in number.

Standard Error

A measure of the dispersion or variability in a sample statistic from the population parameter.

Infinite Population

A theoretical concept where the population size is considered unlimited or endlessly large for statistical analysis.