Polynomial function

Polynomial functions

For example, the function ${\displaystyle f}$, defined by $${\displaystyle f(x)=x^{3}-x,}$$ is a polynomial function of one variable. Polynomial functions of several variables are similarly defined, using polynomials in more than one indeterminate, as in $${\displaystyle f(x,y)=2x^{3}+4x^{2}y+xy^{5}+y^{2}-7.}$$ According to the definition of polynomial functions, there may be expressions that obviously are not polynomials but nevertheless define polynomial functions. An example is the expression ${\displaystyle \left({\sqrt {1-x^{2}}}\right)^{2},}$ which takes the same values as the polynomial ${\displaystyle 1-x^{2}}$ on the interval ${\displaystyle [-1,1]}$, and thus both expressions define the same polynomial function on this interval.