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.

Power function is defined asf:fx=a xn, n can be any real numberIf n is an even integer say n=2k thenfx=a x2kf-x=a -x2k=a x2k=fxHence fx is symmetric about y-axis as fx=f-xThe power function fx=x3 has a special name cubic parabola

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