Question

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.

Answer 1

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%=
`(5)/(100)=0.05`
8%=
`(8)/(100) =0.08`

Next, we know for our problem that your sales commission will be 5% if you sell up to $100,000. So, if
`x` represents the amount that you sell each month, the first equation of our piece wise function will be
`0.05x`
`x \leq 100000`.
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
`0.08x`
`x\ \textgreater \ 100000`.

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