ABSTRACT
It is useful to classify the functions that we know, or will soon know, in an informal way. The polynomials are functions of the form
a0 + a1x+ a2x 2 + · · ·+ ak−1xk−1 + akxk ,
where a0, a1, . . . , ak are constants. This is a polynomial of degree k. A rational function is a quotient of polynomials. For example,
r(x) = 3x3 − x+ 4 x2 + 5x+ 1
is a rational function. A transcendental function is one that is not a polynomial or a rational func-
tion. The elementary transcendental functions are the ones that we encounter
in calculus class: sine, cosine, logarithm, exponential, and their inverses and combinations using arithmetic/algebraic operations.
