Hey guys, Steffi here. Sorry for the late post. Today I will be explaining to you what we have learned last Monday.

Going Backwards with Transformation

In the previous posts, you have learned transforming y = f (x)   to   y = 2 f  (x-3) + 2.

Today, we will learn how to graph it backwards from y = 2 f (x-3) +2   to   y = f (x). And to do that, we will do all the steps in reverse. 

Example (Graph): Consider the transformed function below as y = 2 f (x-3) + 2. How would             y = f (x) be shown?

Step 1: Figure out the transformation performed on y = f (x) to get y = 2 f (x-3) + 2
     

       X-values                                                      

• add 3 to all x-values

       Y-values

• multiply all y-values by 2
• then, add 2 to all y-values 

Step 2: Reverse (do opposite) the transformations and its order, so that we could get f (x)

       X-values

• subtract 3 to all x-values

       Y-values

• subtract 2 to all y-values
• then, divide all y-values by 2 or multiply by 1/2

Therefore, f (x) would look like this:

To check if f (x) is right, get all the points of f (x) and then perform all the transformations ( in step 1) to get 2 f (x-3) +2.

* Since the values in the table for both y=f(x) and y=2f(x-3)+2 match their corresponding graphs, then the graphed f(x) must be right.


Example (Algebraically): If y=3f 2(x-1) -1 = (3,-4), then what is f(x)?

In this example, you are given coordinates for y=3f 2(x-1) -1, so you are trying to find the coordinates for f(x). The steps for this example are stated above.

Step 1:   x-values:                                          

• multiply by 1/2
• then, add by 1

             y-values:

• multiply by 3
• then, subtract by 1

Step 2: Do the Reverse and apply to get the coordinates for f(x)

             x-values:                                                    

• subtract by 1                 ------>   x=3  ---->  3-1 = 2(2) =  4
• then, multiply by 2

             y-values:

• add by 1                       ------>  y= -4  ---->  -4+1 = -3/3 =  -1 
• then, divide by 3

Therefore,   f(x) = (4,-1)

Thank you.. I hope this can be a help to you...