Continue..... power function

Continue..... power function At u Fig. 1.1S If n — integer, power functions have a meaning also at x < O, but their graphs have different forms depending on that is n an even or an odd number. In Fig. 1.16 two such power functions are shown: for n = 2 and n = 3. At n = 2 the function is even and its graph is symrnetric relatively an axis Y; at n = 3 the function is odd and its graph is symmetric relatively an origin of coordinates. The func- tion y = x is called a cubic parabola. On Fig. 1.17 the function y = ±N/G is represented. This function is inverse to the quadratic parabola y = x2, its graph is received by rotating the quadratic parabola graph around a bisector of the I -st coordinate angle. We see by the graph.

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) T h e p o w e r f u n c t i o n f (x) = x^{3} h a s a s p e c i a l n a m e c u b i c p a r a b o l a

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