Real Functions: Power Functions
An power function is a function expressed by xn for positive integer n greater than 1. The graphical representation of power functions is dependent upon whether n is even or odd.
For even values of n (i.e., n = 2, 4, 6, ...), power functions they will resemble the form illustrated for f (x) = x2 depicted below:
For even values of n (i.e., n = 2, 4, 6, ...), f (−x) = (−x)n = xn = f (x) for all x.
Similarly, odd values of n greater than 1 (i.e., n = 3, 5, 7, ...), power functions will resemble the form illustrated for f (x) = x3 depicted below:
Similarly, odd values of n greater than 1 (i.e., n = 3, 5, 7, ...), power functions will resemble the form illustrated for f (x) = x3 depicted below:
For odd values of n greater than 1 (i.e., n = 3, 5, 7, ...), f (−x) = (−x)n = −xn = −f (x) for all x.