On this page we are looking a functions of one variable, usualy denoted by x, in the next section we will look at functions of many variables.
A polynomial has powers of the variable x multiplied by coefficients.
For instance, as the variable is x, the powers are: x, x2, x3, x4 ...
So an example of a polynomial is:
f(x) = a0+ a1 x + a2 x2+ a3 x3+ a4 x4
A polynomial with powers up to x2 is a quadratic, quadratics occur frequently in equations of motion, solving quadratic equations is explained here.
Polynomials of infinite length can represent functions like trig functions (sin, cos, tan) therefore we can use an infinite series to calculate a value of these functions to any accuracy required as explained here.
Linear Functions
There are two ways to define linear functions, some definitions allow a constant offset and some don't.
f(x) = a * x + b
or
f(x) = a * x
The second definition is an example of a linear map or linear operator. We can extend this for several variables as explained on this page.
