please help

Question

Explain how the graph of f(x)=(-2)/(x-3)^2 can be obtained from the graph of y=1/x^2 by means of translations, compressions, expansions, or reflections

Answer 1

(1) Translations:     f(x+c) => translates graph c units to the left

                            

                             f(x-c) => translates graph c units to the right

 

   f(x) = 1/x²     ==>     f(x-3) = 1/(x-3)²     ==>     graph translated 3 units to the right

 

(2) Reflections:     -f(x)  =>  reflects graph about the x-axis

                

                           f(-x)  =>  reflects graph about the y-axis

 

   f(x-3) = 1/(x-3)²     ==>     -f(x-3) = -1/(x-3)²     ==>     graph reflected about the x-axis

 

(3) Expansions/Compressions:     c·f(x)  =>  if c>1, graph stretches in the y-direction

                                                                 if 0<c<1, graph is compressed (in y-direction)

 

                                                 f(cx)  =>  if c>1, graph compresses in the x-direction

                                                                if 0<c<1, graph is stretched (in x-direction)

 

-f(x-3) = -1/(x-3)²   ==>   2·(-f(x-3)) = -2f(x-3) = -2/(x-3)²   ==>   graph stretches in y-directions

 

So, from     f(x)= 1/x²    to     -2f(x-3) = -2/(x-3)² 

   the graph of the original function is shifted (translated) 3 units to the right, flipped (reflected) about the x-axis, and stretched (expanded) in the y-direction.