AMC 10 Step by Step
Log inSign up
2019 AMC 10BProblem 9P1-10~3 minPrint
FunctionsNumber PropertiesSplit into exhaustive cases and handle eachTest small/specific values or special cases to find or verify the answer

The function ff is defined by f(x)=⌊∣x∣⌋−∣⌊x⌋∣f(x) = \lfloor|x|\rfloor - |\lfloor x \rfloor| for all real numbers xx , where ⌊r⌋\lfloor r \rfloor denotes the greatest integer less than or equal to the real number rr . What is the range of ff ?

Log in to save your progress.

Similar problems

Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.