that there are different forms of functions, which is based on the current functions and analytic geometry and geometry, I told you he presented the simplest form, I hope you understand the essenceHey point1967.

What exactly are you trying to convey in your PDF?

the current form of the function - y=f(x) one variable , y=f(x

Function point ( y ) of the independent variables x and the dependent variable

x1 ( function , which is dependent on the independent variables x )

no hybridization functions

y=A-B ( y=x-x1 ) , y=x-( 2x+1) x>-1 , y=B-A ( y=x1 -x) , y=( 2x+1)-x x<-1

- positive hybridization of the first and second functions points

As you long as you are specifying functions that take some inputs and map them to a unique output then everything has already been considered.

The decomposition of the function can be whatever you want to be but as long as you can actually get an output value that is unique then nothing you stated is actually new.

How exactly is this idea different or new?

current function y=3x+5 , Independent variables (3x) , operation ( +) constant ( 5) y dependent variable .

function point , given independent variable ( B=x ) and constant ( A=6 ) , should find the conditions for operation(?) for straihgt line ( AB)

1.Number line

2.Plane , Descartes Coordinate System , 6 ( y coordinate ) , x ( x coordinate )

Number line , in the picture below ( x=7 ) , operation (-) , has two solutions y(straight line)=x(point B)-6(point A) and y(straight line)=6(point A)-x(point B)

Plane , in the picture below ( x=7 ) , operation (+ , 6

A=a , B=x , AB=y , y=|a-x| or y=|x-a|

example

a=5 , x=(2,5,10)

y=|5-2|=3 or y=|2-5|=3 , length straight AB=3

y=|5-5|=0 or y=|5-5|=0 , no straight AB

y=|5-10|=5 or y=|10-5|=5 , length straight AB=5

we have the number line , on it is straight line AB , point A anywhere of number line , point B anywhere of number line , how to describe this as a function ?

example

a=5 , x=(2,5,10)

y=|5-2|=3 or y=|2-5|=3 , length straight AB=3

y=|5-5|=0 or y=|5-5|=0 , no straight AB

y=|5-10|=5 or y=|10-5|=5 , length straight AB=5

we have the number line , on it is straight line AB , point A anywhere of number line , point B anywhere of number line , how to describe this as a function ?

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A=x$_1$ , B=x$_2$ , AB=y , y=|x$_1$ - x$_2$| or y=|x$_2$ - x$_1$|

example

x$_1$ =(2,8) , x$_2$=(-10,-20)

y=|2-(-10)|=12 , length straight AB=12

y=|2-(-20)|=22 , length straight AB=22

y=|8-(-10)|=18 , length straight AB=18

y=|8-(-20)|=28 , length straight AB=28

second solution

A=x , B=y$_1$=f(x) , AB=y$_2$ , y$_2$=|x-f(x)| or y$_2$=|f(x)-x|

example

x=(3,7) , f(x)=3$x^2$-2

y=|3-(27-2)|=22 , length straight AB=22

y=|7-(147-2)|=138 , length straight AB=138

Comment - the structure of the current function: the dependent variable (y) of n independent variables (x$_n$).

here we have a new structure functions: x independent variable, dependent variable y$_1$ (depending on x), y$_2$ dependent variable (depending on x and depends on y$_1$ (f (x))

continuation - dynamic graphics, static graphics, partial graph y=|a-x| ?

y = a-xAgain, what is your point?

The graph of the current solution:

x-coordinate represents all real numbers, when solved function we have two numbers (y, x) , introduces the new coordinates y perpendicular to the x-coordinate and cut the number 0 (plane), the number of y is transferred to the y-coordinate , line (which is parallel to the y-coordinate, and on it is a point that is the number x) is cut from the line (which is parallel to the x-coordinate and it is a point that is the number y) gets the point in the plane (x, y)

which means that the point (x, y) on the x-coordinate of the mapped into a point in the plane (x, y) points are merged to obtain a graph

y = | a-x |

Graph of my solution:

x-coordinate represents all real numbers, when solved function we have three numbers (a, y, x), introduces the new coordinates y perpendicular to the x-coordinate and cut the number 0 (plane), the number of y is transferred to the y-coordinates, lines (the first parallel to the y-coordinate, and on it is a point that is the number a , the second is parallel to the y-coordinate, and on it is a point that is the number x) is cut from the line (which is parallel to the x-coordinate and it is the point which is also the number y) gave the points in the plane (x, y) and (a, y) of the connecting point is obtained straight line

which means that the points (a, x, y) on the x-coordinates are mapped onto the straight line AB in the plane (A (x, y) B (s, y)), the straight line are merged to obtain the graph of

Dynamic graph: x solution

\(\displaystyle x\rightarrow-\infty\) - semi-line

(\(\displaystyle x\rightarrow-\infty\))>x>0- straight line

x=0 -point

0<x(\(\displaystyle x\rightarrow+\infty\))- straight line

\(\displaystyle x\rightarrow+\infty\) semi-line

reads : semi-line ( \(\displaystyle x\rightarrow-\infty\)) , passes into straight line ((\(\displaystyle x\rightarrow-\infty\))>x>0) reduces the length , exceeds the point ( x=0 ) , goes straight line and changes in direction and increases the length (0<x(\(\displaystyle x\rightarrow+\infty\)), straight line the semi-line passes into (\(\displaystyle x\rightarrow+\infty\))

y=|3-x| , x=(1 ,2,3 ,4.5 ) , red color to the solution

https://d6pdkg.bn1302.livefilestore.com/y2pACwy55yirOLiZi0H3m8XnyyEOk93yzUDghUmpduv7myHXERbzqs7SfA3H1Ad-bmBZx6Z5qXPhYeBlL67ukK8TfKQg9_GGtyP0elDDzl11XPpCQb0jJah8mAjfbXRcQfSlGTec6uQjiitSiHD2QgTgQ/sse.png?psid=1

Dynamic graph: y solution

y=0 - point

0<y<(\(\displaystyle y\rightarrow+\infty\)) - straight line

\(\displaystyle y\rightarrow+\infty\) - line

reads : point ( y=0) passes into straight line ( 0<y<(\(\displaystyle y\rightarrow+\infty\)) and increases the length of the , passes straight line the line (\(\displaystyle y\rightarrow+\infty\))

y=( 0 , 1 , 2 ) , red color to the solution

https://qhdrnq.bn1302.livefilestore.com/y2pdCDw3NM3sXSGTVGEjzFBHxFXe3vpM8FvXeHk3KR27lo_DW-QeCaDUWh4g6GU3C6E76we1E7rOcftFiQo2VO2d--mkt3i_qxzFYuaGz_wC6G2LBAfvGRcfmCzas78SV_0Gh16t4i6FZOMEbwOZVzSnA/ssp.png?psid=1

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