Question

The graph of the function f(x)=1/(x−3) −12 is a transformation of the graph of the function g(x)=1/x.Find the horizontal and vertical shifts.

Answer 1

`\begin{gathered} f(x)=(1)/((x-3))-12 \\ g(x)=(1)/(x) \end{gathered}`

f(x) has a vertical asymptote at x = 3, while g(x) has a vertical asymptote at x = 0.

f(x) has a horizontar asymptote at y = -12, while g(x) has a horizontal asymptote at y = 0.

Therefore, the graph of f(x) is the graph of g(x) shifted 12 units down and 3 units right