Concept:
Basic polynomial functions, also called power functions, are functions of the form f(x)=xn for whole numbers n. Power functions have distinctive shapes for even and odd powers, and are the building blocks of general polynomials.
Basic Polynomial Functions
f(x)=
xn
f(x) = x
INSTRUCTIONS
Choose a power for the power function you wished to see graphed by using the slider on the right, or by entering the desired value directly in the exponent field. You may enter any whole number value from 0 to 10. The corresponding power function will appear to the left, and a smaller graph centered on the origin will also be supplied.
EXPLORATIONS
Exploration 1: Why do the even power functions and the odd power functions look different?
Exploration 2: Under what condition or conditions does raising a number to larger and larger powers result in smaller and smaller results?
