Asymptotic Functions
Some functions change concavity without having points of inflection. Instead, they can change concavity around vertical asymptotes or discontinuities. Take, for example, the function 2x2/(x2 – 1). It is concave up when |x| > 1 and concave down when |x| < 1. However, it has no points of inflection because 1 and -1 are not in the domain of the function.
Read more about this topic: Inflection Point
Famous quotes containing the word functions:
“When Western people train the mind, the focus is generally on the left hemisphere of the cortex, which is the portion of the brain that is concerned with words and numbers. We enhance the logical, bounded, linear functions of the mind. In the East, exercises of this sort are for the purpose of getting in tune with the unconscious—to get rid of boundaries, not to create them.”
—Edward T. Hall (b. 1914)