Consider the function f graphed here: 
For what values of a does 
not exist?
Definitions:
Dreams
A sequence of thoughts, images, and sensations occurring in a person's mind during sleep.
NREM Sleep
A phase of sleep characterized by non-rapid eye movement, consisting of stages 1-3, each deeper than the last, and associated with physical and mental restoration.
REM Sleep
A unique phase of sleep characterized by rapid eye movements, low muscle tone, and vivid dreams, playing a key role in emotional regulation and memory.
Vivid Dreams
Highly detailed, clear, and sometimes intensely emotional dreams that are remembered upon awakening.
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