What is function?

Answer 1

A function is a self contained algorithm to do a mathematical operation. You give it a name and pass it parameters and it returns a result.

For example a function called DATE may have month, day, and year as parameters and return a serial number. A function FV may have parameters present value, interest, and term, and return the future value of an investment.

Answer 2

A function is a relationship between y and x such that:

1. y is dependent on x.
2. y is continuous over the domain of x.
3. there is a unique y for each x.

y = x^2 is a function, because it meets all criteria.
y = (x)^1/2 is not a function, because if x = 4, y = 2 or y = -2.
y = sqrt(x) is a function, because sqrt(x) is always positive, so at x = 4, y = 2 only.

Answer 3

A function is an abstract entity that associates an input to a corresponding output according to some rule. In other words it describes the intuitive idea of deterministic dependence of one quantity (the input) to another (the output).
f(x)->y
f means it is a function of x (which is the input) and then this is mapped onto y according to the function.

Answer 4

"A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities"
In other words, a function is a formula (i.e. a rule) which can be set up any way whatsoever.

When studying functions we commonly use the letter f to denote the function itself and the letter x to denote the variable. g and h are often used as well lik f(x),g(x),h(x)

Answer 5

It is a relation between two non-empty sets such that EVERY element in the first set relates ONE AND ONLY ONE element in the second set