jmc

Question

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 1.) What is the sum of the x-coordinates of all points where f(x) = x+1?

Accepted Answer

We superimpose the graph of y=x+1 on the same axes as the original graph: FIGURE There are three intersections, at (-2,-1), (1,2), and (4,5). The sum of their x-coordinates is (-2)+1+4=3.