An algebraic function is a type of mathematical function defined by a polynomial equation. It can be expressed in the form f(x) = a_n x^n + a_n-1 x^n-1 + \ldots + a_1 x + a_0 , where a_n, a_n-1, \ldots, a_0 are constants and n is a non-negative integer. The output of an algebraic function is determined by substituting values of x into the equation. Algebraic functions can be classified into different types, such as linear, quadratic, cubic, and higher-degree functions. Each type has its own characteristics and graphs, which can be analyzed using tools from algebra and calculus. These functions are fundamental in various fields, including physics, engineering, and economics.