How is the the graph of y=1/2x-6

obtained from the graph of y=1/x
?
A) Vertically stretched by a factor of 2 and shifted right by 3 units.
B) Vertically stretched by a factor of 3 and shifted right by 2 units.
C) Horizontally stretched by a factor of 2 and shifted left by 3 units. <my answer
D) Horizontally compressed by a factor of 2 and shifted right by 3 units.

1 answer

1/(2x-6) = 1/2 * 1/(x-3)
so, shifted right 3 and vertically shrunk by 2.

Hmmm. Not a choice. So, equivalently,

1/(2x-6) = 1/(2(x-3))

shifted by 3, horizontally shrunk by 2.
(D)

http://www.wolframalpha.com/input/?i=plot+y%3D1%2Fx,+y%3D1%2F(2x-6)