Decreasing Function

Pronunciation: /dɪˈkris ɪŋ ˈfʌŋk ʃən/ ?

graph of f(x)=e^(1/x) which decreases from left to right.
Figure 1: Decreasing function

A decreasing function is a function whose values become smaller as the argument of the function increases.[1] The graph of a decreasing function descends from upper left to lower right. Figure 1 shows the graph of the function

f(x)=e^(1/x)

A function can also be decreasing on a subset of the domain of the function. This is usually called increasing on an interval or decreasing on an interval. Figure 2 shows the graph of y = -x2+3. This function is increasing on the interval from negative infinity to 0. This function is also decreasing on the interval from 0 to infinity.

The function y=-x^2+3 which increases on the interval (-infinity,0] and decreases on the interval [0,infinity).
Figure 2: Increasing and decreasing on an interval.

References

  1. decreasing. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2010-01-22). http://www.merriam-webster.com/dictionary/decreasing.
  2. Slaught, H. E. and Lennes N. J.. Elementary Algebra, pg 315. Allyn and Bacon, 1915. (Accessed: 2010-01-22). http://www.archive.org/stream/elementaryalgebr00slaurich#page/315/mode/1up/search/decreasing.

Cite this article as:


Decreasing Function. 2010-01-22. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/decreasingfunction.html.

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2010-01-22: Added "References" (McAdams, David.)
2008-12-04: Initial version (McAdams, David.)

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