What does an algebraic function look like?
An algebraic function is (roughly) a function that satisfies a polynomial equation the coefficients of which are themselves polynomials. So, polynomials and rational functions are algebraic functions, but so too are things such as square root. e.g., y^2-x=0 is a quadratic in y with polynomial coefficients in x, thus y=sqrt(x) is an algebraic function. As always, you have to be careful to prescribe the domain of definition before the ‘formula’ is a ‘function’. (In some ways this definition is like the definition of an algebraic number, which is a number that satisfies a polynomial equation with integer coefficients.) Wikipedia is good on this.
