Continue power function

Continue power function Fig. Lis if n — integer. power functions have a meaning alw at O. but their graphs have different forms depending that is n an even or an odd number. In Fig. 1.16 two such -ower functions are shown: for n 2 and n = 3. At n = 2 the function is even and its graph is symmetric _elatively an axis Y; at n = 3 the function is odd and its graph symmetric relatively an origin of coordinates. The func- tion y = .r3 is called a cubic parabola. — is represented. This On Fig. 1.17 the function y — function is inverse to the quadratic parabola y = , its graph received by rotating the quadratic parabola graph around bisector of the I-st coordinate angle. We see by the

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Power function means f (x) = x^{n} is called power function . If n is positve integer, then f (x) = x^{n} is defined for all values of x i . e . x \in R e . g . f (x) = x^{2} or f (x) = x^{3} is defined for x \in R If n \in Even Natural Number, then f (x) is called even function and if n \in Odd Natural Number, then f (x) is called odd function . Even functions are symmetric about y - axis and odd function are symmetric about origin . e . g .

In case of f (x) = x^{n} when n is negative integer, then f (x) is defined for x \in R - \{0\} e . g . f (x) = \frac{1}{x^{2}} is defined for x \in R - \{0\} .

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