{"status": "success", "data": {"description_md": "The function $f$ is defined by $$f(x) = \\lfloor|x|\\rfloor - |\\lfloor x \\rfloor|$$for all real numbers $x$, where $\\lfloor r \\rfloor$ denotes the greatest integer less than or equal to the real number $r$. What is the range of $f$?\n\n$\\textbf{(A) }$  $\\{-1, 0\\}$\n$\\textbf{(B) }$  $\\text{The set of nonpositive integers}$\n$\\textbf{(C) }$  $\\{-1, 0, 1\\}$\n$\\textbf{(D) }$  $\\{0\\}$\n$\\textbf{(E) }$  $\\text{The set of nonnegative integers}$", "description_html": "<p>The function  <span class=\"katex--inline\">f</span>  is defined by  <span class=\"katex--display\">f(x) = \\lfloor|x|\\rfloor - |\\lfloor x \\rfloor|</span> for all real numbers  <span class=\"katex--inline\">x</span> , where  <span class=\"katex--inline\">\\lfloor r \\rfloor</span>  denotes the greatest integer less than or equal to the real number  <span class=\"katex--inline\">r</span> . What is the range of  <span class=\"katex--inline\">f</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) }</span>    <span class=\"katex--inline\">\\{-1, 0\\}</span> <br/>\n <span class=\"katex--inline\">\\textbf{(B) }</span>    <span class=\"katex--inline\">\\text{The set of nonpositive integers}</span> <br/>\n <span class=\"katex--inline\">\\textbf{(C) }</span>    <span class=\"katex--inline\">\\{-1, 0, 1\\}</span> <br/>\n <span class=\"katex--inline\">\\textbf{(D) }</span>    <span class=\"katex--inline\">\\{0\\}</span> <br/>\n <span class=\"katex--inline\">\\textbf{(E) }</span>    <span class=\"katex--inline\">\\text{The set of nonnegative integers}</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 1, "problem_name": "2019 AMC 10B Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc10B_p10", "prev": "/problem/19_amc10B_p08"}}