The parent function of the functions of the form f x = x − a + b is f x = x .
Note that the domain of f x = x is x ≥ 0 and the range is y ≥ 0 .
The graph of f x = x − a + b can be obtained by translating the graph of f x = x to a units to the right and then b units up.
Sketch the graph of y = x − 1 + 2 from its parent graph y = x .
Step 1: Draw the graph of y = x .
Step 2: Move the graph of y = x by 1 unit to the right to obtain the graph of y = x − 1 .
Step 3: Move the graph of y = x − 1 by 2 units up to obtain the graph of y = x − 1 + 2 .
The domain of the function y = x − 1 + 2 is x ≥ 1 .
The range of the function y = x − 1 + 2 is y ≥ 2 .
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