Alison S. answered • 03/12/20

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In addition to Ryan S's great response, you can use transformations to determine the vertex of the "V" and surrounding points of this absolute value graph. The vertex of y = abs(x) is the origin. It has been translated two right, from (x-2) and two up (from +2). This gives us a vertex located at (2,2). Now, the leading coefficient is -1, so the magnitude of the slope is 1, and the V has been reflected upside down by the negative value. So, the slope to the left of the vertex is 1, and to the right of the vertex is -1. If x = 0, y = 0, then go up 1 over 1 to arrive at (1,1). Go up 1 over 1 again to arrive at (2,2) which is the vertex we already found. After the vertex, go DOWN 1 over 1 to arrive at (3, 1), and DOWN 1 over 1 again to arrive at (4,0). Plugging in these x values from 0 to 4 into the equation should confirm the y values you just found on the graph. For instance, f(4) = -abs(4-2)+2 = -abs(2)+2 = -2 + 2 = 0.

SOLUTION: (0,0); (1,1); (2,2); (3,1); (4,0)

Of course, there are infinitely many solutions ;-)