A salesperson makes 35000 a year plus 7 commission on all sa

A salesperson makes $35,000 a year plus 7% commission on all sales up to (and including) $250,000. If they exceed $250,000 in sales for a calendar year, the salesperson’s commission jumps to 9% for all their remaining sales over $250,000. The salesperson’s total salary S for a given year is based on their total sales x. Write the piecewise-defined function S(x).

Solution

$35,000 a year plus 7% commission on all sales up to (and including) $250,000

-----> S(x) for x< $250,000 : $35,000+0.07x

If they exceed $250,000 in sales for a calendar year, the salesperson’s commission jumps to 9% for all their remaining

---->S(x) for x>$250,000 :$35000 + 0.09x

S(x) = $35,000+0.07x for x<= 250,000

= $35000 + 0.09x for x>250,000