Describing Transformations of Linear Functions

We are given the graphs of $f(x)$ and $g(x)$ on a coordinate plane, and want to describe the transformation from the graph of $f(x)$ to the graph of $g(x).$ Let's find some corresponding points in the graphs and measure the distance between them.

We see that the graph of $g(x)$ is a horizontal translation $2$ units left of the graph of $f(x).$ We can also see this using the function rules. The function $g(x)$ can be written on the form $y=f(x-h).$ $g(x)=f(x+2) \quad \Leftrightarrow \quad g(x)=f(x-(\text{-} 2))$ In our function, we have that $h=\text{-} 2.$ This means the graph of $g(x)$ is a horizontal translation $2$ units left of the graph of $f(x).$