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:

CNS

Stands for Central Nervous System, which includes the brain and spinal cord, responsible for processing and sending out information throughout the body.

Blood-Brain Barrier

A protective mechanism that controls the passage of substances from the bloodstream into the brain tissue.

Central Nervous System

The complex network of the brain and spinal cord that serves as the primary processing center for nervous system activity and coordination.

Peripheral Nervous System

The division of the nervous system outside the brain and spinal cord, including sensory and motor neurons.