Graphing Square Root Functions

The parent function of the functions of the form is .

Note that the domain of is and the range is .

The graph of can be obtained by translating the graph of to a units to the right and then b units up.

Example:

Sketch the graph of from its parent graph .

Solution:

Step 1: Draw the graph of .

Step 2: Move the graph of by 1 unit to the right to obtain the graph of .

Step 3: Move the graph of by 2 units up to obtain the graph of .

The domain of the function is .

The range of the function is .