Asymptotes and axis intercepts of a rational function and the range after a vertical stretch

The function \(f\) is defined by \(f(x)=\dfrac{3x-6}{x+2}\) for \(x\in\mathbb{R}\), \(x\neq-2\). The diagram shows the graph of \(y=f(x)\) together with its asymptotes.

1. Find the equation of
   1. the vertical asymptote of the graph;
   2. the horizontal asymptote of the graph.[3]
2. Find the coordinates of each point at which the graph of \(y=f(x)\) meets the \(x\)-axis and the \(y\)-axis.[4]

The function \(g\) is defined by \(g(x)=2x\) for \(x\in\mathbb{R}\).

3. 1. Describe fully the single transformation that maps the graph of \(y=f(x)\) onto the graph of \(y=(g\circ f)(x)\).
   2. Hence write down the range of \(g\circ f\).[5]