GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)  


10:01 Nov 25, 2018 
English to Polish translations [PRO] Science  Mathematics & Statistics / statystyka kliniczna  


 
 Selected response from: Frank Szmulowicz, Ph. D. United States Local time: 00:24  
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Summary of answers provided  

3  model funkcji potęgowej 

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 
 
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