Question

PLS HELP pls explain im confused

The first hour is free.
The second to sixth hour is $4 per hour.
After six hours, the cost is $2.50 per hour.
Complete the table below to represent the context as a piecewise function:

Answer 1

f(x) = 4x 1 < x ≤ 6

f(x) = 2.50x x > 6

(Also see image attached)

Explanation:

The function f(x) is the cost for x hours of whatever work

Considering the 3 rows of the table, the first row has already been filled in and it states that if the number of hours is one or less, the cost is 0

We have to fill in the rest

2nd to sixth hour is 4 per hour so this can be represented as

f(x) = 4x 1 < x ≤ 6
Essentially this states that if the number of hours is more than 1, the cost is $4 per hour pro-rated if necessary)

For the last row we have
f(x) = 2.50x x > 6

Note that the tricky part here is trying to figure out when the second hour starts. The second hour starts immediately after passage of exactly one hour Thus if the total time worked is 1 hour and 15 minutes, you will still be charged for the 15 minutes over and above the first hour is $4 per hour. That means you will be charged for 15 minutes which is 1/4th of the second hour and this will cost you $1