Abusiness banker works on commission based on the amount of loans made. he
earns 5% on all loans made below $5000. he then begins earning 10% commission
until he hits $50,000 in loans. beginning with $50,000 his commision jumps to 15% for
all remaining loans. find a piecewise function for the banker's commission on the total loans of x dollars.

Step-by-step explanation:

Well first let's see what they would look like if they weren't piecewise.  

If all commissions were 5%, and we say the loan amount is x, the commission then is .05x.  Similarly, 10% is .1x and 15% is .15x  Now we just need to incorporate these into a piecewise form.

We are breaking up the piecewise function into what x is.    the three groups are $0-$4,999, $5,000-49,999 and $50,000 and higher.  So basically we just write this out.

We will have to put these in terms of inequalities so 0 ≤ x ≤ 4,999, 5,000 ≤ x ≤ 49,999 and 50,000 ≤ x  Now!  we're set.

basically you're just going to list these off like f(x) = .05x when 0 ≤ x ≤ 4,999 and similarly list the other two.  Do you know how it is supposed to look?