power model

Polish translation: model funkcji potęgowej

GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)
English term or phrase:power model
Polish translation:model funkcji potęgowej
Entered by: Frank Szmulowicz, Ph. D.

10:01 Nov 25, 2018
English to Polish translations [PRO]
Science - Mathematics & Statistics / statystyka kliniczna
English term or phrase: power model
PK variables over the dose ranges tested may be investigated using a power model.
kgas
Poland
Local time: 06:24
model funkcji potęgowej
Explanation:
Propozycja.

cccccc
Funkcja potęgowa – funkcja postaci y = x^a, gdzie a jest daną liczbą rzeczywistą.
https://pl.wikipedia.org/wiki/Funkcja_potęgowa

cc
Power functions
Real functions of the form {\displaystyle f(x)=cx^{n}} {\displaystyle f(x)=cx^{n}} with {\displaystyle c\neq 0} c\neq 0 are sometimes called power functions.[citation needed] When {\displaystyle n} n is an integer and {\displaystyle n\geq 1} n\geq 1, two primary families exist: for {\displaystyle n} n even, and for {\displaystyle n} n odd. In general for {\displaystyle c>0} c>0, when {\displaystyle n} n is even {\displaystyle f(x)=cx^{n}} {\displaystyle f(x)=cx^{n}} will tend towards positive infinity with increasing {\displaystyle x} x, and also towards positive infinity with decreasing {\displaystyle x} x. All graphs from the family of even power functions have the general shape of {\displaystyle y=cx^{2}} {\displaystyle y=cx^{2}}, flattening more in the middle as {\displaystyle n} n increases.[13] Functions with this kind of symmetry ( {\displaystyle f(-x)=f(x)} {\displaystyle f(-x)=f(x)}) are called even functions.

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

For {\displaystyle c<0} c < 0, the opposite asymptotic behavior is true in each case.[14]

https://upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Po...
https://en.wikipedia.org/wiki/Exponentiation#Power_functions
Selected response from:

Frank Szmulowicz, Ph. D.
United States
Local time: 00:24
Grading comment
Dziękuję!
4 KudoZ points were awarded for this answer



Summary of answers provided
3model funkcji potęgowej
Frank Szmulowicz, Ph. D.


  

Answers


3 hrs   confidence: Answerer confidence 3/5Answerer confidence 3/5
model funkcji potęgowej


Explanation:
Propozycja.

cccccc
Funkcja potęgowa – funkcja postaci y = x^a, gdzie a jest daną liczbą rzeczywistą.
https://pl.wikipedia.org/wiki/Funkcja_potęgowa

cc
Power functions
Real functions of the form {\displaystyle f(x)=cx^{n}} {\displaystyle f(x)=cx^{n}} with {\displaystyle c\neq 0} c\neq 0 are sometimes called power functions.[citation needed] When {\displaystyle n} n is an integer and {\displaystyle n\geq 1} n\geq 1, two primary families exist: for {\displaystyle n} n even, and for {\displaystyle n} n odd. In general for {\displaystyle c>0} c>0, when {\displaystyle n} n is even {\displaystyle f(x)=cx^{n}} {\displaystyle f(x)=cx^{n}} will tend towards positive infinity with increasing {\displaystyle x} x, and also towards positive infinity with decreasing {\displaystyle x} x. All graphs from the family of even power functions have the general shape of {\displaystyle y=cx^{2}} {\displaystyle y=cx^{2}}, flattening more in the middle as {\displaystyle n} n increases.[13] Functions with this kind of symmetry ( {\displaystyle f(-x)=f(x)} {\displaystyle f(-x)=f(x)}) are called even functions.

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

For {\displaystyle c<0} c < 0, the opposite asymptotic behavior is true in each case.[14]

https://upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Po...
https://en.wikipedia.org/wiki/Exponentiation#Power_functions

Frank Szmulowicz, Ph. D.
United States
Local time: 00:24
Native speaker of: Native in EnglishEnglish, Native in PolishPolish
PRO pts in category: 157
Grading comment
Dziękuję!
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