Question

. The following piecewise function gives the cost, c (x) 35.50when x ≤4 c (x )= { 35.50+5.25 ( x−4) when x>4 } , of a classified ad in a car magazine. A. Is the cost of one line the same as the cost of four lines? B. What is the cost of 8 lines?

Answer 1

The cost function for the classified ad is a piecewise function, with a flat rate for up to 4 lines and an additional charge per line above that. The cost for up to four lines is a flat rate of $35.50, and the cost for 8 lines is $56.50.

Step-by-step explanation:

The student's question relates to a piecewise function describing the cost of a classified ad in a car magazine. The cost function c(x) behaves differently based on the number of lines x used in the ad:

• For x ≤ 4, the cost is a flat rate of $35.50.
• For x > 4, the cost includes the flat rate plus an additional $5.25 for each line above 4.

Part A: Cost of One Line vs. Four Lines

Since the cost is a flat rate of $35.50 for up to 4 lines, the cost of one line is the same as the cost of four lines.

Part B: Cost of 8 Lines

To find the cost of 8 lines, we use the second part of the function where x > 4: c(8) = 35.50 + 5.25(8 - 4) = 35.50 + 5.25(4) = 35.50 + 21.00 = $56.50.