Marked as Best Answer
(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/x^{2} ==> 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/x^{2} 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.