write a function rule modeling the state income tax owed by a person whose taxable income is no more than $20,000.

This is a step function:
The function f(x) that models the state income tax for a person whose taxable income is no more than $20,000 is:
[tex]f(x)=\begin{cases}0.03x;\text{ 0}\leq x<20,000 \\ \\ 0.03(20,000);\text{ }x\ge20,000\end{cases}[/tex]