AMC 10 Step by Step
Log inSign up
Printable

2019 AMC 10B Problem 9

Include the solutionBack to the problem
2019 AMC 10B Problem 9AMC 10 Step by Step
Name:                             Date: September 13, 2026
Functions · difficulty 2 of 5 · about 3 min · position P1-10

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 ?

  1. A)

    {−1,0}\{-1, 0\}

  2. B)

    The set of nonpositive integers\text{The set of nonpositive integers}

  3. C)

    {−1,0,1}\{-1, 0, 1\}

  4. D)

    {0}\{0\}

  5. E)

    The set of nonnegative integers\text{The set of nonnegative integers}

Working