Graph y=|x-3|

Problem

y=|x−3|

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−3 Setting x−3=0 gives x=3 indicating a shift of 3 units to the right.

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

4. Calculate additional points to determine the slope of the two rays. For x>3 the equation is y=x−3 (slope of 1). For x<3 the equation is y=−(x−3) or y=−x+3 (slope of -1).

5. Plot key points such as (2,1) (3,0) and (4,1) and connect them to form the "V" shape.

Final Answer

y=|x−3|

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