Question

A hardware store will deliver up to 6 items for a $25 delivery charge. There is
a charge of $4 for each additional item to be delivered.

Write a piecewise function for the cost of
having x items delivered.

I understand the answer is 25 for x <= 6 and 4x + 1 for x > 6. But how do you get the 4x + 1?

Answer 1

charge=25 if x<7
charge=25+(x-6)*4 if x>7

which is correct.

Now your first answer, 25 for x<=6 is the same as 25 for x<7
You you cannot have decimal portions of items, so it goes from six to 7.

The second answer is just plain wrong.

for instance, if one had 7 item, the charge would be 29 dollars.
Your formula says 17 dollars for seven items. Nuts to your answer given.