Example LF.FORM.1: Visualize $f(x)=2x+3$ with a mapping
diagram that illustrates the slope $= m=2$ and the Y-intercept is
Find the X-intercept for $f$ and visualize this on the mapping
diagram as well.
Draw a mapping diagram yourself or use the GeoGebra figure.
Given a point / number, $x$, on the source line, there is a unique
arrow meeting the target line at the point / number, $2x + 3$,
which corresponds to the linear function's value for $x$
When the point in the domain is $0$, the arrow points to $f(0) = 3$
visualizing the "Y-intercept" or "initial value" of $f$.
Check the box "Show Second Pair" to consider $f(1)= 5$ then the difference in the value of $f$ for
a unit change in $x$ is $f(1)-f(0) = 5-3=2.$
Since a unit step 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.
As $m > 0$, the arrows never cross illustrating that the
function is increasing at a rate of 2 units on the target
value for every unit increase in the domain value.
The X- intercept is the value $a$ on the domain axis for which $f(a)=0$ and from which the
arrow hits the number $0$ on the target. For this function,
that value is $a=-\frac 3 2$. You can check this by checking the box "Show a where f(a) = 0 " and entering $-\frac
3 2$ for $a$ on the GeoGebra figure.