Describe the Transformations and Give the Equation for the Graph $f ( x ) = | x |$

question 178

Multiple Choice

Describe the transformations and give the equation for the graph.
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• A) It is the graph of \(f ( x ) = | x |\) translated 6 units to the left, stretched vertically by a factor of 2 and translated 4 units down. The equation is \(y = 2 | x + 6 | - 4\)
• B) It is the graph of \(f ( x ) = | x |\) translated 6 units to the left, shrunken vertically by a factor of \(\frac { 1 } { 2 }\) and translated 4 units down. The equation is \(y = \frac { 1 } { 2 } | x + 6 | - 4\)
• C) It is the graph of \(f ( x ) = | x |\) translated 6 units to the left, shrunken vertically by a factor of \(\frac { 1 } { 2 }\) and translated 4 units down. The equation is \(y = \frac { 1 } { 2 } | x - 6 | - 4\)
• D) It is the graph of \(f ( x ) = | x |\) translated 6 units to the left, stretched vertically by a factor of 2 and translated 4 units down. The equation is \(y = 2 | x - 6 | + 4\)

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Definitions:

Accommodation

In cognitive psychology, the process of altering one's existing schemas, or ways of thinking, as a result of new information or experiences.

Equilibration

The process by which individuals balance assimilation and accommodation to create stable understanding in cognitive development.

Symbolic Image

A representation that stands in for something else, conveying meaning through association or resemblance, often used in communication and thought processes.

Simple Organized Pattern

A basic and structured arrangement or sequence of elements or actions.