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Function

here I’m going to define function, examples and mathematics insight

Definitions

function, in mathematics, an expression, rule, or law, that defines a relationship between one variable (the independent variable/input) and another variable (the dependent variable/output). Generally it is denoted by, f(x), g(x),and h(x).

y=f(x)

If a variable y depends on a variable x in such a way that each value of x determine exactly one of y, then we say that y is a function of x

A function f is a rule that associates a unique output with each input. If the input is denoted by x, then the output denoted by f(x) (read as “ f of x” )

Examples

1. let A be the area and r be the radius of the circle, A =4 pi r^2 where, A is dependent variable while r is independent variable
2. let x is input a number of the real set and y is output also be the real set, X=X^3 where , X=x, y=x^3

• the set "x" is called the Domain,
• the set "y" is called the Codomain, and
• the set of elements that get pointed to in Y (the actual values produced by the function) is called the Range.

Mathematics insight

with the start of big figure of mathematics, function have probably important and key way to learn the mathematical concepts. here I’m going to insert a visualizes function interpretation.

Here still we’ve learn variable/ input, don’t b confuse with the word argument, input may b numerical number or argument whatever the mean is same. further more, I try to quick click on mine at single view here attach visualization of function.

Another useful and important thinking about function, it is hard to cover all concept one by one I try to my best. All those thing will be discourse some how the non mathematician feel that going on.

Ordered pairs

for this, we use the Cartesian coordinate system to represent the function, I try to represent above mention information to be use.

Write the input and output of a function as an "ordered pair",
They are called ordered pairs because the input always comes first, and the output second:  (input, output)   So it looks like this:  ( x, f(x) )

Note the graph of the function is not discuses here,

Next, blog about types of function and graphical representation of function

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