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

question 133

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

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Definitions:

Absorption Costing

A costing method that includes all manufacturing costs - direct materials, direct labor, and both variable and fixed manufacturing overhead - in the cost of a unit of product.

Fixed Manufacturing Overhead

Ongoing expenses that do not change in total with the level of production or sales volume, such as salaries, rent, and insurance, associated specifically with the manufacturing process.

Variable Costing

An accounting method that includes only variable costs—those that change with production levels—in the cost of goods sold and inventory valuation.

Unit Product Cost

The total cost associated with producing one unit of a product, including direct materials, direct labor, and allocated overhead.