Draw a mapping diagram yourself or have SAGE create this by evaluating.

Given a point / number, $x$, on the source line, there is a unique arrow meeting the target line at the point / number, $3 + 2*(x-1) = 2x + 1$, which corresponds to the linear function's value for $x$

When the point in the domain is $1$, the black arrow points to $f(1) = 3$ visualizing the point $(1,3)$ on the graph of $f$. We also have$f_{+ 3} \circ f_{*2} \circ f_{ -1} (1) = f_{+3} \circ f_{*2}(0)= f_{+3}(0) = 3$ which is visualized in the mapping diagram for the composition by arrows $1 \rightarrow 0 \rightarrow 0 \rightarrow 3$ .

Since a unit step on the source axis is used in this mapping diagram, we see the slope (magnification, rate) visualized in the gap between the heads of consecutive arrows on the mapping diagram both in the middle section and the final arrows.

As $m > 0$, the arrows never cross. Observe also that the function is increasing at a rate of two units on the second and third target values for every unit increase in the domain value.