Do piecewise functions have parent functions?

What is the parent function of higher order polynomial functions (degree greater than 3)?

• How does it look on a graph? What is the standard form of polynomial functions? Help I seriously have no idea :// This is for my final exam project.

• Answer:

  Historically y = x^n has been called the parent function of polynomials. However that really never felt good to mathematicians (I am a mathematician with a doctorate) who felt that the following should be the parent function. 0 ∑ (a(n) * x^n) n In other words (a(n) * x^n) + ((a(n-1) * (x^(n-1))...a(0) * x^(0) (and, of course x^0 = 1. Here there is no general graph. By now the majority of mathematicians are of the view that "parent functions" are a nonsensical concept meant for teaching, but more confusing than useful. They (I'm one of this group) feel that there is no such thing as a parent function. We feel that it's like a six-legged horse - you can write down "parent function" but it has no meaning. Wow - confusion. I I were you I'd probably go with the oldest defintion: y = x^n. The graphs of functions where n is odd look quite similar and different from the graphs of y = x^n where n is even which look quite similar. I'll graph some for you. These are some odd parent functions: http://i369.photobucket.com/albums/oo133/gerryrains/Odd-Parent_functions.jpg These are some even parent functions: http://i369.photobucket.com/albums/oo133/gerryrains/Even_Parent_Functions.jpg This is probably what your teacher wants. Remember, he's not a real mathematician. .