point.ms
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see the attachment
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TeeEm
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(Original post by point.ms)
see the attachment
I read it and I got very scared

next ...
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point.ms
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(Original post by TeeEm)
I read it and I got very scared

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have you figured something out

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TeeEm
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(Original post by point.ms)
have you figured something out

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nothing whatsoever ...
I was hoping you will tell us.
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point.ms
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(Original post by TeeEm)
nothing whatsoever ...
I was hoping you will tell us.
have a geometric object straight line a(AB) , make free movement of point B , you will get different values a , This procedure is applied to the numerical line ( point A and B are located on the numerical line ) , and it should be shown an algebraic , you will get the function y(straight line a)=a(point A)-x(point B) or y(straight line a)=x(point B)-a(point A) , y=a-x or y=x-a



have a geometric object straight line a(AB) , make free movement of point A and B , you will get different values a , This procedure is applied to the numerical line ( point A and B are located on the numerical line ) and it should be shown an algebraic , you will get the function
y(straight line a)=x(point A)-f(x)(point B) or y(straight line a)=f(x)(point B)-x(point A) , y=x-f(x) or y=f(x)-x
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point.ms
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form function points, the Pythagorean theorem as part of the function (90 degrees)
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tombayes
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(Original post by point.ms)
form function points, the Pythagorean theorem as part of the function (90 degrees)
do you have a question?
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point.ms
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(Original post by tombayes)
do you have a question?


solution of the task -


we have the numerical line , on it is straight line AB , point A is located on a number of numerical line , point B anywhere of numerical line , how to describe this as a function ?
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point.ms
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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 ?
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point.ms
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first solution
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)=3x^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| ?
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point.ms
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y = a-x
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
x\rightarrow-\infty - semi-line
(x\rightarrow-\infty)>x>0- straight line
x=0 -point
0<x(x\rightarrow+\infty)- straight line
x\rightarrow+\infty semi-line
reads : semi-line ( x\rightarrow-\infty) , passes into straight line ((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(x\rightarrow+\infty), straight line the semi-line passes into (x\rightarrow+\infty)
y=|3-x| , x=(1 ,2,3 ,4.5 ) , red color to the solution
https://d6pdkg.bn1302.livefilestore....sse.png?psid=1

Dynamic graph: y solution
y=0 - point
0<y<(y\rightarrow+\infty) - straight line
y\rightarrow+\infty - line
reads : point ( y=0) passes into straight line ( 0<y<(y\rightarrow+\infty) and increases the length of the , passes straight line the line (y\rightarrow+\infty)
y=( 0 , 1 , 2 ) , red color to the solution
https://qhdrnq.bn1302.livefilestore....ssp.png?psid=1
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point.ms
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static graphics
Ap and Aq semi-line and surface between them
https://o9alca.bn1302.livefilestore..../ss.png?psid=1
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