The graph of f(x) = 1/x^2 is vertically compressed by a factor of 1/2 units , then shifted to the left 5 units and down 4 units.

G(x)=

Transformation involves moving a function from one position to another. The resulting function g(x) is:

Given that:

See attachment for vertical compression

When the function is shifted 5 units left, the rule is:

So, we have:

When the function is shifted 4 units down, the rule is:

So, we have:

Hence, the resulting function is:

Read more about transformations at:

link

  G(x) = (1/2)(1/(x +5)^2 -4

Step-by-step explanation:

G(x) = bf(x -h) +k

represents the function f(x) shifted right h units, up k units and scaled vertically by a factor of b. Your problem statement tells you ...

  f(x) = 1/x^2, b = 1/2, h = -5, k = -4

so your G(x) is ...

  G(x) = (1/2)(1/(x +5)^2 -4

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: