In the United States, personal income taxes are paid according to a specific scale. For example, individuals who earn a yearly salary between $31,000 and $31,150 must pay $4229 in taxes. Individuals who earn a yearly salary between $41,000 and $41,150 must pay $6381 in taxes. (Source: irs.gov) Which type of function would best model this situation: a step function or a piecewise function that is not a step function? Explain.

Question

In the United States, personal income taxes are paid according to a specific scale.  For example, individuals who earn a yearly salary between $31,000 and $31,150 must pay $4229 in taxes.  Individuals who earn a yearly salary between $41,000 and $41,150 must pay $6381 in taxes.  (Source:  irs.gov) Which type of function would best model this situation: a step function or a piecewise function that is not a step function?  Explain.

joannablackwelder · Answer

I think this would best be modeled by a step function since as x increases y stays the same for a while, then jumps up to the next value and stays there a while again. I know that is not explained very eloquently, but I hope it helps. :)