Analyze the Graph of the Given Function F as Follows $| x |$

question 54

Essay

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.
- $f ( x ) = x ^ { 3 } - 0.4 x ^ { 2 } - 2.5861 x + 3.0912$

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Definitions:

Organism

A living entity characterized by the capacity for metabolism, growth, reaction to stimuli, and reproduction.

Differentiation

The process of identifying and emphasizing the unique characteristics or features of something or someone.

Inner Cell Mass

The mass of cells inside the embryonic blastocyst, from which the embryo and eventually the fetus develop.

Endoderm

Cells of the inner cell mass of the embryo that develop into the digestive system and the lungs.