Editing Exponentiation (section)

===Power functions===
{{Main|Power law}}

[[File:Potenssi 1 3 5.svg|thumb|left|Power functions for {{math|1=''n'' = 1, 3, 5}}]]
[[File:Potenssi 2 4 6.svg|thumb|Power functions for {{math|1=''n'' = 2, 4, 6}}]]

Real functions of the form <math>f(x) = cx^n</math>, where <math>c \ne 0</math>, are sometimes called power functions.<ref>{{cite book |last1=Hass |first1=Joel R. |last2=Heil |first2=Christopher E. |last3=Weir |first3=Maurice D. |last4=Thomas |first4=George B. |title=Thomas' Calculus |date=2018 |publisher=Pearson |isbn=9780134439020 |pages=7–8 |edition=14}}</ref> When <math>n</math> is an [[integer]] and <math>n \ge 1</math>, two primary families exist: for <math>n</math> even, and for <math>n</math> odd. In general for <math>c > 0</math>, when <math>n</math> is even <math>f(x) = cx^n</math> will tend towards positive [[infinity (mathematics)|infinity]] with increasing <math>x</math>, and also towards positive infinity with decreasing <math>x</math>. All graphs from the family of even power functions have the general shape of <math>y=cx^2</math>, flattening more in the middle as <math>n</math> increases.<ref name="Calculus: Early Transcendentals">{{cite book |last1=Anton |first1=Howard |last2=Bivens |first2=Irl |last3=Davis |first3=Stephen |title=Calculus: Early Transcendentals |date=2012 |publisher=John Wiley & Sons |page=[https://archive.org/details/calculusearlytra00anto_656/page/n51 28] |isbn=9780470647691 |edition=9th |url=https://archive.org/details/calculusearlytra00anto_656 |url-access=limited}}</ref> Functions with this kind of [[symmetry]] {{nobr|(<math>f(-x)= f(x)</math>)}} are called [[even functions]].

When <math>n</math> is odd, <math>f(x)</math>'s [[asymptotic]] behavior reverses from positive <math>x</math> to negative <math>x</math>. For <math>c > 0</math>, <math>f(x) = cx^n</math> will also tend towards positive [[infinity (mathematics)|infinity]] with increasing <math>x</math>, but towards negative infinity with decreasing <math>x</math>. All graphs from the family of odd power functions have the general shape of <math>y=cx^3</math>, flattening more in the middle as <math>n</math> increases and losing all flatness there in the straight line for <math>n=1</math>. Functions with this kind of symmetry {{nobr|(<math>f(-x)= -f(x)</math>)}} are called [[odd function]]s.

For <math>c < 0</math>, the opposite asymptotic behavior is true in each case.<ref name="Calculus: Early Transcendentals"/>