Write the Word or Phrase That Best Completes Each Statement $f ( x ) = 2 x ^ { 4 } - 7 x ^ { 3 } + 11 x - 4$

question 20

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.
-For the polynomial function $f ( x ) = 2 x ^ { 4 } - 7 x ^ { 3 } + 11 x - 4$
a) Find the $x$ - and $y$ -intercepts of the graph of $f$ . Round to two decimal places, if necessary.
b) Determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept.
c) End behavior: find the power function that the graph of $f$ resembles for large values of $| x |$ .
d) Use a graphing utility to graph the function.Approximate the local maxima rounded to two decimal places, i necessary. Approximate the local minima rounded to two decimal places, if necessary.
e) Determine the number of turning points on the graph.
f) Put all the information together, and connect the points with a smooth, continuous curve to obtain the graph

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Definitions:

Awake Adults

Referencing the state of alertness and consciousness in adult individuals during periods they are not sleeping.

Spinal Cord

A long, thin, tubular structure made up of nervous tissue, which extends from the brainstem down the back, enclosed in the spinal canal.

Filum Terminale

A fibrous tissue extension of the conus medullaris of the spinal cord, anchoring it within the vertebral canal.

Conus Medullaris

The tapered, lower end of the spinal cord which typically ends at the first or second lumbar vertebra, marking the transition from spinal cord to cauda equina.