Identify the Parent Function and the Transformation Shown in the Graph

question 108

Multiple Choice

Identify the parent function and the transformation shown in the graph. Write an equation for the function shown in the graph.

• A) Reflection in the \(x\)-axis of \(y = | x | ; y = - | x + 2 |\)
• B) Reflection in the \(y\)-axis of \(y = | x | ; y = - | x - 2 |\)
• C) Reflection in the \(y\)-axis of \(y = | x + 2 | ; y = - | x + 2 |\)
• D) Reflection in the \(x\)-axis of \(y = | x - 2 | ; y = - | x - 2 |\)
• E) Horizontal shift of \(x\)-axis of \(y = | x + 2 | ; y = - | x + 2 |\)

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Definitions:

NMR Spectroscopy

A technique that uses nuclear magnetic resonance to determine the molecular structure of organic compounds by observing the interaction of atomic nuclei with radio waves.

N-H Functionally

Refers to compounds containing nitrogen-hydrogen bonds that have distinct properties or roles in chemical reactions, often related to base or nucleophile behavior.

Basicity

A measure of an entity’s ability to accept protons, often related to the strength of bases in chemical reactions.

Alkyl Groups

Hydrocarbon groups derived from alkanes by removing one hydrogen atom, often represented generically as R-, and used as substituents in organic chemistry.