A vertical stretch/compression is given by the transformation below
[tex]\begin{gathered} h(x)\rightarrow a*h(x) \\ a>1\rightarrow\text{ stretch by a factor of a} \\ 0And a vertical shift is given by the following transformation[tex]\begin{gathered} h(x)\rightarrow h(x)+b \\ b>0\rightarrow\text{ b units up} \\ b<0\rightarrow\text{ b units down} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} f(x)=x\rightarrow\frac{1}{3}x\Rightarrow\text{ vertical compression by a factor of 3} \\ \frac{1}{3}x\rightarrow\frac{1}{3}x-1=g(x)\rightarrow\text{ vertical shift 1 unit down} \end{gathered}[/tex]