IN MATH: 1. n. A function's values for extreme values of its variable; the value a function, f(x) approaches when x is extremely large or when x is extremely small; the function value, f(x) or y, approximated by the value of another function defined by the curve which is approached but never "reached" by a graph.

IN ENGLISH: 1. as defined above.
EX. 1: When x is extremely large, the values of f(x) are close to the values of y = 0, so, f(x) is positive and approximately 0. When x is extremely small, the values of f(x) are close to the values of y = 0, so, f(x) negative and approximately 0.  
EX. 2: When x is extremely large, the values of f(x) are close to the values of y = 4, so, f(x) is approximately 4. When x is extremely small, the values of f(x) are close to the values of y = 4, so, f(x) negative and approximately 4.  
EX. 3: When x is extremely large, the values of f(x) are close to the values of y = x + 4, which is increasing infinitely, so, f(x) is increasing to positive infinitely. When x is extremely small, the values of f(x) are close to the values of y = x + 4, which is decreasing infinitely, so, f(x) is decreasing to negaive infinity.  
EX. 4: When x is extremely large, the values of f(x) are close to the values of y =  x² + 4, which is increasing infinitely, so, f(x) is decreasing to negaive infinitely. When x is extremely small, the values of f(x) are close to the values of y =  x² + 4, which is decreasing infinitely, so, f(x) is decreasing to negaive infinity.  
APPLICATION: See list 230.
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