Question 1028572
 

<pre>

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

 {{{y=2/(4x+3)^2}}}{{{""-""}}}{{{1}}}

We factor 4 out in the parentheses in the denominator,
in spite of the fact that it involve a fraction:
 
{{{y=2^""/(4(x+3/4))^2}}}{{{""-""}}}{{{1}}} 

Then we square the 4

{{{y=2^""/(16(x+3/4)^2)}}}{{{""-""}}}{{{1}}}

Then we cancel the 2 into the 16
 
{{{y=1^""/(8(x+3/4)^2)}}}{{{""-""}}}{{{1}}} 

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

{{{y=expr(1^""/8^"")*(1/(x+3/4)^2)}}}{{{""-""}}}{{{1}}}

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

Now we can begin the transformations:

{{{y=1/x^2}}} to {{{y=expr(1^""/8^"")*(1/(x+3/4)^2)}}}{{{""-""}}}{{{1}}}

Begin with this red graph: {{{graph(300,300,-5,5,-5,5,1/x^2)}}}


Shift left by 3/4 by replacing {{{x}}} by {{{(x+3/4)}}}

{{{y=1/(x+3/4)^2)}}}

That's this green graph: {{{graph(300,300,-5,5,-5,5,1/x^2,1/(x+3/4)^2))}}}

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

{{{y=expr(1^""/8^"")*(1/(x+3/4)^2)}}}

That's this blue graph: {{{graph(300,300,-5,5,-5,5,1/x^2,1/(x+3/4)^2,1/(8(x+3/4)^2)))}}}

Shift downward 1 unit by subtracting 1 from the whole right side:
 
{{{y=expr(1^""/8^"")*(1/(x+3/4)^2)}}}{{{""-""}}}{{{1}}}

That's this wine-colored graph at the bottom: {{{graph(300,300,-5,5,-5,5,1/x^2,1/(x+3/4)^2,1/(8(x+3/4)^2),-1+1/(8(x+3/4)^2)))}}}
 
Edwin</pre>