Question

a salesperson makes a base salary of $1000 per month. once he reaches $10,000 in total sales, he earns an additional 4% commission on the amount in sales over $10,000. write a piecewise - defined function to model the salespersons total monthly salary (in $) as a function of the amount in sales x.

Explanation:

Step1: Define base salary case

When sales $x \leq 10000$, the salary is the fixed base amount.
$S(x) = 1000$ for $0 \leq x \leq 10000$

Step2: Define commission case

When sales $x > 10000$, salary is base + 4% commission on sales over $10000$.
$S(x) = 1000 + 0.04(x - 10000) = 1000 + 0.04x - 400 = 600 + 0.04x$ for $x > 10000$

Answer:

$$S(x)=
LATEXBLOCK0
$$