Graph the following function using transformation techniques. $g(x)=\frac{-2}{x-1}$

Step 1 ：The function $g(x)=\frac{-2}{x-1}$ is a transformation of the function $f(x)=\frac{1}{x}$, which is a hyperbola with a vertical asymptote at $x=0$ and a horizontal asymptote at $y=0$.

Step 2 ：The negative sign in front of the 2 in the function $g(x)$ reflects the graph of $f(x)$ over the x-axis. This means that the graph of $g(x)$ will be a downward opening hyperbola.

Step 3 ：The 2 in the numerator of the function $g(x)$ stretches the graph of $f(x)$ vertically by a factor of 2. This means that the graph of $g(x)$ will be narrower than the graph of $f(x)$.

Step 4 ：The $-1$ in the denominator of the function $g(x)$ shifts the graph of $f(x)$ to the right by 1 unit. This means that the vertical asymptote of the graph of $g(x)$ will be at $x=1$.

Step 5 ：Putting all these transformations together, we can sketch the graph of $g(x)$ as a downward opening hyperbola, narrower than the graph of $f(x)$, and shifted 1 unit to the right.

Step 6 ：Finally, we should check our graph against the original function $g(x)=\frac{-2}{x-1}$ to make sure it meets all the requirements of the problem.