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

question 327

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

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Definitions:

Indifference Curves

Graphical representations in microeconomics to illustrate different combinations of two goods between which a consumer is indifferent.

Optimal Choice

The most efficient, beneficial, or highest utility decision or selection from among multiple alternatives given the available information.

Budget Constraints

The limitations on the consumption bundles that a consumer can afford based on their income and the prices of goods.

Hamburger

A favored culinary option that includes a grilled or fried patty made from minced meat, typically beef, encased within a cut-open bun and frequently accompanied by a range of sauces and additional ingredients.