SOLUTION: Find the sequence of transformations which takes the graph y=1/x^2 to y=2/(4x+3)^2 -1

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Question 1028572: Find the sequence of transformations which takes the graph
y=1/x^2 to y=2/(4x+3)^2 -1

Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20086)   (Show Source): You can put this solution on YOUR website!
My solution is below. Edwin McCravy = AnlytcPhil
Answer by AnlytcPhil(1810)   (Show Source): You can put this solution on YOUR website!


Before we can do the transformations, we must change the 
form of the final result to show the shrinking and 
shifting required:

 

We factor 4 out in the parentheses in the denominator,
in spite of the fact that it involve a fraction:
 
 

Then we square the 4



Then we cancel the 2 into the 16
 
 

Then we consider the division by 8 as a multiplication
by 1/8:



 ----------------------------------------

Now we can begin the transformations:

 to 

Begin with this red graph: 


Shift left by 3/4 by replacing  by 



That's this green graph: 

Shrink by a factor of 1/8, a shrink because 1/8 < 1



That's this blue graph: 

Shift downward 1 unit by subtracting 1 from the whole right side:
 


That's this wine-colored graph at the bottom: 
 
Edwin

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