A state has just adopted the following state income tax system :

Question

no tax on the first $10,000 earned, 1% of the next $10,000 earned, 2% of the next $20,000 earned, Write a multiline function for T(x), the state income tax due on earnings of x dollars.

Answer 1

T(x)=0 (for 0≤x≤10000)

T(x)=0.1(x-10000)=0.1x-1000 (for 10000<x≤20000)

T(x)=1000+0.2(x-20000)=0.2x-3000 (for x>20000)

Though not asked for, the graph illustrates the function.

The graph shows continuous T for varying values of x, where the scale is 1=$1000.

EXAMPLE: When x=$40000, T=$5000 and when x=$65000, T=$10000. The domain of x is x≥0.