If we're speaking about mathematical functions, then this kind of function can be mono-variable or multi-variables and can or cannot have parameters.

f(x1,x2,x3...xn)=a, is a multi-variable function

x1,x2,x3...xn-variables which can be real or complex numbers

a-parameter

In analytic geometry, the argument of the function is called "parameter".

In mathematics, the name "variable" is usually met in description of a function (in the equations is called "unknown").

The mathematical variables are written with the help of Roman or Greek letters, but the most common are "x,y,z". The importance of using variables in mathematics is that a relationship can be formulated in a general way, no matter the value of variable is.

In mathmatical related sciences we often come accross the parameters and varibles.

A parameter for a particular value determines a particular function.

For different values of the parametrs we get a family of functions.

The variable for for values gives the paticular values of the paricular function.For the entire domain of the variable it defines a particular function.

Example:

y=5**x**+ **c**. Here c is a parameter. x is a variable.

y=5x + c reprepresents a family of parallel straight lines ,all having a slope of 5 ,for different values of c. for c=1, y=5x+1 is one member this family of straight lines.

x is a vaiable. For a particular value of x=5, we get a particular functional value of the function y= 5x+1 and that value is 5*5+1=26.

For all values of the variable x, y = 5x+1 represents a particular function. In fact in y=5x+c is also a member of the family of functions y=mx+c for parmetric value of m=5.

x^2+y^2=a^2 represents a family functions: y = **+**or**- **{Square root (x^2-a^2)}

For different values of a ,the parameter, we get a family of concentric circles but with different radii.

Hope this helps.