I just completed Trigonometry and College Algebra, and i'm heading into Calculus, so i thought i would get a head start on the material. So right now i'm working out of an old calculus book i got at the library. Then i came across this problem: A dial-direct long distance call between two cities costs $1.04 for the first 2 minutes and $0.36 for each additional minute or fraction thereof. a.) Use the greatest integer function to write the cost C of a call in terms of the time t (in minutes). Graph the cost function and discuss its continuity. b.) Find the cost of a 9-minute call. I didn't think this would be so hard, so i worked at it a little bit, the only part i had trouble with was coming up with the correct function, graphing and solving for 9 minutes is easy after that. I got: C(t) = 1.04, 0 < t <= 2 1.04 + 0.36 * greatest integer of (t - 2 ), t > 2 So i doulble checked in the back of the book and it says the answer is: C(t) = 1.04, 0 < t <= 2 1.04 + 0.36 * greatest integer of (t - 1), t > 2, t is not an integer 1.04 + 0.36(t - 2), t > 2, t is an integer i don't understand why there needs to be to seperate functions for it being an integer or not. I thought with greatest integer, if the number is already an integer, it would leave it alone, and also, why only t - 1 in the second one, shouldn't it be t - 2? Anyways, i hope someone will help me out. Thanks!