Graph y=|x-2|

Problem

y=|x−2|

Solution

1. Identify the parent function as the absolute value function y=|x| which has a characteristic "V" shape with a vertex at (0,0)

2. Determine the horizontal shift by looking at the expression inside the absolute value, x−2 Setting x−2=0 gives x=2 indicating a shift of 2 units to the right.

3. Locate the vertex of the graph at the point (2,0)

4. Calculate additional points to determine the slopes of the two rays. For x>2 the equation is y=x−2 (slope of 1). For x<2 the equation is y=−(x−2) or y=−x+2 (slope of -1).

5. Plot key points such as (1,1) (2,0) and (3,1) and draw two rays extending from the vertex to form the "V" shape.

Final Answer

y=|x−2|

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