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Graphing Square Root Functions

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.

Example:

Sketch the graph of y = x 1 + 2 from its parent graph y = x .

Solution:

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 .