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.
a. Write a piecewise function for the cost of
having x items delivered.
b. What is the charge to have 14 items delivered?
c(x) =
25 for 0 < x <= 6
25 + 4⌊x-6⌋ for x>6
a. To write a piecewise function for the cost of having x items delivered, we need to consider the different scenarios based on the number of items.
If x ≤ 6 (up to 6 items), the delivery charge is a fixed $25, regardless of the number of items. Therefore, for this range, the function is:
f(x) = $25
If x > 6 (more than 6 items), there is a $25 delivery charge for the first 6 items, and an additional charge of $4 for each additional item. So, for this range, the function is:
f(x) = $25 + ($4 × (x - 6))
b. To find the charge for the delivery of 14 items, we need to determine if it falls within the range of up to 6 items (x ≤ 6) or more than 6 items (x > 6).
In this case, 14 is more than 6, so we use the second part of the piecewise function:
f(x) = $25 + ($4 × (x - 6))
Substituting x = 14:
f(14) = $25 + ($4 × (14 - 6))
f(14) = $25 + ($4 × 8)
f(14) = $25 + $32
f(14) = $57
Therefore, the charge to have 14 items delivered would be $57.