You are employed at a company in which commission rates are based on how much you sell. if you sell up to $100,000 of merchandise in a month, you earn 5% of sales as a commission. if you sell over $100,000 you earn 8% commission on your sales. write a piecewise function that gives the amount you earn in commission in a given month for x dollars in sales.

First, we are going to convert your sales commissions from percentages to decimals. To do that we are going to divide each one by a 100%:
5%=
8%=

Next, we know for our problem that your sales commission will be 5% if you sell up to $100,000. So, if  represents the amount that you sell each month, the first equation of our piece wise function will be  .
Similarly, we know that your sales commission will be 8% if you sell more than $100,000; therefore, the second equation of our piecewise function will be  .

Now, lets put all together to create our picewise function: