Sketch $$y=|x-2|\quad\text{and}\quad y=4-|x-2|$$ on the same axes. Find their intersection points. F

Question

Sketch $$y=|x-2|\quad\text{and}\quad y=4-|x-2|$$ on the same axes. Find their intersection points. Find the vertices of the region enclosed by the graphs. Calculate the area of the enclosed region.

Accepted Answer

(a) Intersections $(0,2),(4,2)$; (b) Other vertices $(2,0),(2,4)$; (c) Area $8$ square units.

Modulus Function

Modulus Function