Example OAF.PFF.4 : $P(x) =\frac 1 2*x^2*(x-2)^2*(x+1)^3$.
Notice: $A=\frac 1 2, r_1=2$ , and $r_2 = -1$ and the factor $x^2$ has the root $r=0$ with multiplicity $2$.
Draw a mapping diagram and graph of $P$ yourself or explore the GeoGebra figure.

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

When the point in the domain is $0$, the arrow points to $f(0) = 0$  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 are $a=0$,  $a=2$ and $a=-1$, the values of $r_1$, $r_2$ and $r$.