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 \(f(x) = 1.8\)?
+128407 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
