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The complete graph of \(y=f(x)\), which consists of five line segments, is shown in red below. (On this graph, the distance between grid lines is .)

What is the sum of the x-coordinates of all points where \(f(x) = 1.8\)?

 



 

 Mar 17, 2019
 #1
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Assuming that the grid lines are 1 uint apart......f(x) = 1.8  will occur three times

 

The first line where this occurs is one with a slope of 2 and contains the point  (1, 2)

So...the equation of this line is  f(x) = 2(x - 1) + 2  =  2x

So.....

1.8 = 2x

1.8 / 2 = x  =   9/10

 

The next line where this occurs has a slope of - 1 and also contains the point (1,2)

So......the equation of this line is  f(x)  =  -(x - 1) + 2   =   -x + 3

So....

1.8 = -x + 3

-1.2 = -x

1.2 = x  =  12/10

 

The final occurrence  is on  the line with the same slope as the first and contains the point (2, 1)

So.....the equation of this line is  f(x)  = 2(x - 2) + 1  =  2x - 3

So....

1.8 = 2x - 3

4.8 = 2x

2.4 = x = 24/10

 

 

 

So...the sum of the x coordinates  = 9/10 + 12/10 + 24/10  =  45/10  =  4.5

 

 

cool cool cool

 Mar 17, 2019

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