Determine the Domain and the Range $F ( x ) = \frac { x ^ { 3 } + 6 } { x ^ { 3 } - 2 }$

question 16

Multiple Choice

Determine the domain and the range. $F ( x ) = \frac { x ^ { 3 } + 6 } { x ^ { 3 } - 2 }$

• A) domain: \(( - \infty , \sqrt [ 3 ] { 2 } ) \cup ( \sqrt [ 3 ] { 2 } , \infty )\) ; range: \(( - \infty , \infty )\)
• B) domain: \(( - \infty , \sqrt [ 3 ] { 2 } ) \cup ( \sqrt [ 3 ] { 2 } , \infty )\) ; range: \(( - \infty , 1 ) \cup ( 1 , \infty )\)
• C) domain: \(\left( - \infty , 2 ^ { 3 } \right) \cup \left( 2 ^ { 3 } , \infty \right)\) ; range: \(( - \infty , 1 ) \cup ( 1 , \infty )\)
• D) domain: \(( - \infty , - \sqrt [ 3 ] { 2 } ) \cup ( - \sqrt [ 3 ] { 2 } , \infty )\) ; range: \(( - \infty , \infty )\)
• E) domain: \(( - \infty , \sqrt [ 3 ] { 2 } ) \cup ( \sqrt [ 3 ] { 2 } , \infty )\) ; range: \(( - \infty , 0 ) \cup ( 0 , \infty )\)

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Definitions:

Subliminal Stimulation

The exposure to stimuli below the threshold of conscious awareness, purportedly influencing thoughts, feelings, or behaviors without overt perception.

Bottom-up Processing

A way of processing information in which the brain forms perceptions by starting with individual pieces of sensory data and combining them to create a cohesive image or understanding.

Context Effects

The influence of environmental factors on one's perception or understanding of a stimulus.

Perceptual Set

A readiness to perceive or interpret stimuli in a particular way based on expectations, experiences, emotions, and culture.