a company awards its salespeople 3% commission on sales below $20,000, 3.5% commission on sales from $20,000 to $30,000, and 4% commission for sales over $30,000. What's the piecewise function that shows the commission for x dollars in sales?
Let's denote the commission for x dollars in sales as f(x). We can create the piecewise function with the following three cases:
Case 1: Sales below $20,000
For sales below $20,000, the commission is 3% of the sales.
f(x) = 0.03x, for 0 < x ≤ 20000
Case 2: Sales from $20,000 to $30,000
For sales in the range from $20,000 to $30,000, the commission is 3.5% of the sales.
f(x) = 0.035x, for 20000 < x ≤ 30000
Case 3: Sales over $30,000
For sales over $30,000, the commission is 4% of the sales.
f(x) = 0.04x, for x > 30000
Putting it all together, we have the piecewise function:
f(x) = 0.03x, for 0 < x ≤ 20000
f(x) = 0.035x, for 20000 < x ≤ 30000
f(x) = 0.04x, for x > 30000