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

question 8

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

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Definitions:

Budget Constraint

A representation of all the combinations of goods and services that a consumer can afford with a fixed income and prices.

Indifference Curve

A graph representing different bundles of goods between which a consumer is indifferent, showing combinations that give the consumer the same level of satisfaction.

Income

The amount of money or its equivalent received during a period of time in exchange for labor, goods, or services, or as profit on capital.

Indifference Curves

Graphical representations in economics showing combinations of goods among which a consumer is indifferent, helping to analyze consumer choices.