Example OAF.PFF.2 :  $P(x) =\frac 1 2*(x-2)^2*(x+1)^3$.

Draw a mapping diagram and graph of $P$ yourself or explore 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, $P(x) =\frac 1 2*(x-2)^2*(x+1)^3$, which corresponds to the polynomial function's value for $x$

When the point in the domain is $0$, the arrow points to $P(0) = 2$ visualizing the "Y-intercept" on the graph of $P$.
The X- intercepts are the values for $a$ on the domain axis from which the arrow hits the number $0$  on the target. For this function, those values is $a=2$ and $a=-1$, the values of the roots, $r_1$ and $r_2$.