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 \(f(x) = 1.8\)?

Guest Mar 17, 2019

#1**+1 **

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

CPhill Mar 17, 2019