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Graphing by Transformations 
Example 3
Explanation
 

Objectives 


Examples

     
Use transformations to draw the graph of the function .

Make sure that you label at least 3 points on your final graph.

Solution

Step 1: Identify the Basic Graph

The function  is most similar to the Basic Function 
.  So we start with the graph:


 

Three points that capture the basic shape are
( -1 , 1) ; (0, 0) and (1, 1).
 
 


Step 2: Apply each transformation to the Basic Points
  • 1st Transformation 
      •  
      This transformation affects only the x coordinates of the Basic Points.

      In particular, add 4 to each x coordinate.
       

        the point (- 1, 1) becomes the point (3, 1)

        the point (0, 0) becomes the point ( 4, 0)

        the point (1, 1) becomes the point ( 5, 1)

  • 2nd Transformation 

     
      In particular, we multiply each y coordinate by 1/3.
       
        the point (3, 1) becomes the point (3, 1/3)

        the point (4, 0) becomes the point (4, 0)

        the point (5, 1) becomes the point (5, 1/3)

  • 3rd Transformation 

    •  
      In particular, add 2 to each y coordinate.
       
        the point (3, 1/3) becomes the point (3, 7/3)

        the point (4, 0) becomes the point (4, 2)

        the point (5, 1/3) becomes the point (5, 7/3)


Step 3: Plot the final transformed points and connect them with
              the original Basic Shape

So our original graph was shifted 4 units to the right, vertically compressed by a factor of 1/3 and then shifted 2 units up.