Compare the Graph Of $p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9$

question 56

Multiple Choice

Compare the graph of $p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9$ with $p ( x ) = x ^ { 2 }$ .

• A) \(p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9\) shifts right 9 units, shifts downward 9 units, and shrinks by a factor of \(- \frac { 1 } { 9 }\).
• B) \(p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9\) shifts right 81 units, shifts upward 9 units, and shrinks by a factor of \(\frac { 1 } { 9 }\).
• C) \(p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9\) shifts left 9 units, shifts downward 9 units, and shrinks by a factor of \(\frac { 1 } { 9 }\).
• D) \(p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9\) shifts right 9 units, shifts upward 9 units, and shrinks by a factor of \(\frac { 1 } { 9 }\).
• E) \(p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9\) shifts left 81 units, shifts upward 9 units, and shrinks by a factor of \(- \frac { 1 } { 3 }\).

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Definitions:

Demand Curve

A graph showing the relationship between the quantity of a good that consumers are willing and able to purchase and the price of the good.

Marginal Cost

The hike in cost incurred by generating an additional unit of a good or service.

Profit-Maximizing

This is the process by which a firm decides on the price and output level that returns the maximum profit.

Short-Run Monopoly

A situation where one company dominates the market for a certain product or service temporarily, often before new entrants arrive.