Explain power function.

P o w e r f u n c t i o n i s d e f i n e d a s f : ℝ \to ℝ f (x) = a x^{n}, n c a n b e a n y r e a l n u m b e r I f n i s a n e v e n i n t e g e r (s a y n = 2 k) t h e n f (x) = a x^{2 k} f (- x) = a {(- x)}^{2 k} = a x^{2 k} = f (x) H e n c e f (x) i s s y m m e t r i c a b o u t y - a x i s a s f (x) = f (- x) S i m i l a r l y i f p o w e r i s o d d s a y n = 2 k + 1 f (x) = a x^{2 k + 1} f (- x) = a {(- x)}^{2 k + 1} = - a x^{2 k + 1} = - f (x) H e n c e i t i s a n t i s y m m e t r i c a b o u t y - a x i s . I t i s i m a g e a b o u t o r i g i o n

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