Graphing Square Root Functions

The parent function of the functions of the form f x = xa +b is f x = x .

Note that the domain of f x = x is x0 and the range is y0 .

The graph of f x = xa +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= x1 +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= x1 .

Step 3: Move the graph of y= x1 by 2 units up to obtain the graph of y= x1 +2 .

The domain of the function y= x1 +2 is x1 .

The range of the function y= x1 +2 is y2 .