Unit
Polynomial and Rational Functions
Cornell University
PhD. in Mathematics
Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.
A power function is a function where y = x ^n where n is any real constant number. Many of our parent functions such as linear functions and quadratic functions are in fact power functions. Other power functions include y = x^3, y = 1/x and y = square root of x. Power functions are some of the most important functions in Algebra. All power functions pass through the point (1,1) on the coordinate plane.
I want to introduce the idea of a power function. A power function is one of the form Y=X^N where N is any real number constant. A lot of our parent functions are actually power functions, for example, Y=X. One of our simplest functions is a power function where N is 1.
So here N=1. Y=X2, obviously a power function. N=2. Y=X3 . N=3, also a power function. Y=1/X is a power function. Here 1/X is the same as X-1 . So this is a power function with N=-1. And finally, Y= the square root of X. The square root of X is the same as X1/2 . So this is a power function with N=1/2.
Power functions are really important. And a lot of the basic functions we study are power functions. And so it's important to know the definition. One of the things that they all have in common is that they all pass through the point (1, 1). Anyway, power functions, functions of the form Y= X^N