Describing Transformations of Linear Functions

The transformation $a\cdot f(x)$ is a vertical stretch or shrink by a factor of $a,$ where $a>0$ and $a\ne 1.$ This means that the outputs of $g(x)$ are the outputs of $f(x)$ multiplied by $a.$ We can use the fact that $$g(x)=a\cdot f(x)\Rightarrow g(0)=a\cdot f(0)$$ to calculate $a.$ Looking at the graph, we can see that $g(x)$ passes through the point $(0,\text{-}12),$ which means that $g(0)=\text{-}12.$ We can also see that $f(x)$ passes through the point $(0,\text{-}6),$ meaning that $f(0)=\text{-}6.$ We can substitute these into the equation $g(0)=a\cdot f(0).$ The value of $a$ is $2.$