The cost of sending an overnight package from New York to Atlanta is $9.80 for up to, but not including, the first pound and $3.50 for each additional pound (or portion of a pound).A model for the total cost of sending the package is where is the weight of the package (in pounds).Sketch the graph of this function. Note that the function is the greatest integer function.

Question

The cost of sending an overnight package from New York to Atlanta is $9.80 for up to, but not including, the first pound and $3.50 for each additional pound (or portion of a pound).A model for the total cost  of sending the package is   where  is the weight of the package (in pounds).Sketch the graph of this function. Note that the function  is the greatest integer function.

Quizplus · Accepted Answer

The function is defined as: 
- for weight less than 1 pound: $9.80
- for weight between 1 and 2 pounds (inclusive): $9.80 + $3.50 = $13.30
- for weight between 2 and 3 pounds (inclusive): $9.80 + $3.50 + $3.50 = $16.80
- and so on.

The function can also be written using the greatest integer function as:
f(x) = 9.80 + 3.50 * ⌈x - 1⌉ for x > 0

The graph of the function will be a series of line segments with slope 3.50 and y-intercept 9.80 for each interval between consecutive integers. The graph will start at (0,0) and will have a vertical asymptote at x=0.

Among the answer choices, only B matches this description.

The Cost of Sending an Overnight Package from New York