Example: For the function below.  Graph using transformations.

First we must examine the base function

Graph using plotting points.  We can use the standard set of x-values to find ordered pairs.  Substitute the standard set of x-values into the base function to get the base graph.

The graph below shows the points plotted and the line that connects them.  The domain is   and the range is [)

 

Analyze the transformations.

The -3 inside the square shifts the graph right 3 units.

The – in the front of the base reflects the graph over the x-axis.

 

The +4 outside the square shifts the graph up 4 units.

You can see the graph after the transformations.

The domain is   and the range is (]

Here is a video example of a transformation of a square function.