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

question 70

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

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Definitions:

Consumer Surplus

The discrepancy showcasing the difference between the sum consumers are eager to pay and the price eventually paid.

Monopolist

A single seller in a market who has significant control over the price and supply of a good or service, facing little to no competition.

Marginal Cost

The increase in cost incurred by producing one additional unit of a product or service.

Producer Surplus

The difference between what producers are willing to sell a good for and the actual market price they receive, representing a measure of producer welfare.