Draw a mapping diagram and graph with a visualization for $f$ on the
graph and a mapping diagram for $x=0$ and $x_1=1$ or use the diagram created with GeoGebra to explore further.
Mapping Diagram for $ f (x) = 2x + 1$
$x=0,x_1=1$
Graph for $ f (x) = 2x + 1$
On the GeoGebra figure you can move either $x$ or $x_1$ on the mapping diagram. On the mapping diagram, given any two distinct points / numbers, $x$ and
$x_1$, in the domain, the two corresponding arrows will not intersect between
the two axes. On the graph, if $x<x_1$, then the point $(x,f(x))$ will be lower and to the left of $(x_1,f(x_1))$.
Both these visual features are indicative of a increasing
function.
