Question

A cable company wants to provide cell phone service for residents on an island. The function for the cost of laying the cable from the island to the mainland is mc022-1.jpg, where x represents the length of the cable in meters. What are the domain and range of the function?


mc022-2.jpg
domain: all real numbers
range: all real numbers greater than or equal to 17,000
domain: all real numbers greater than or equal to 0
range: all real numbers greater than or equal to 17,000
domain: all real numbers greater than or equal to 0
range: all real numbers greater than or equal to 13,000
domain: all real numbers greater than or equal to 13,000
range: all real numbers greater than or equal to 0

Answer 1

Answer: domain: all real numbers greater than or equal to 0; range: all real numbers greater than or equal to 17,000.

Reason: x is a length so x ≥ 0, and the cost has a fixed minimum (the constant term) of \$17,000, so C(x) ≥ 17,000 (with equality at x = 0).