Decreasing Function

Pronunciation: /dɪˈkris.ɪŋ ˈfʌŋk.ʃən/ Explain

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.[2] 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. McAdams, David E.. All Math Words Dictionary, decreasing function. 2nd Classroom edition 20150108-4799968. pg 55. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. decrease. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 7/3/2018. http://www.merriam-webster.com/dictionary/decreasing. Buy the book
  3. Slaught, H. E. and Lennes N. J.. Elementary Algebra. pg 315. www.archive.org. Allyn and Bacon. 1915. Last Accessed 7/3/2018. http://www.archive.org/stream/elementaryalgebr00slaurich#page/315/mode/1up/search/decreasing. Buy the book

Cite this article as:

 McAdams, David E. Decreasing Function. 4/19/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/decreasingfunction.html.

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Revision History

4/19/2019: Updated equations and expressions to the new format (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/3/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
1/22/2010: Added "References". (McAdams, David E.)
12/4/2008: Initial version. (McAdams, David E.)

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