Yes, there are different types of functions—so many, in fact, that the topic of “functions” is a book in itself. In particular, algebraic equations include polynomial and rational expression functions. For example, polynomial equations include linear (first degree) functions, such as f(x) = 2x; a quadratic (second degree) function example is f(x) = x² (for more about polynomials and degrees, see below).

But “algebraic and polynomial functions” are not the only use of the term “function”—so don’t get confused. There are also non-algebraic functions called exponential functions, and the inverses of exponential functions, called logarithmic functions. Set theory emphasizes the use of functions (for more about functions and sets, see “Foundations of Mathematics”); and there are trigonomic functions that include the relationships of sine, cosine, and tangent functions (for more information about trigonometry, see “Geometry and Trigonometry”). There also are continuous or discontinuous functions, transcendental functions, and even real and complex functions (all this may or may not be connected to algebra). The list goes on, and it is easy to see that mathematicians love the word “function.”