{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"d7a5d53c-fdc4-5271-b464-bb01b0283d87","task_key":"intermediate~5falgebra--test--d7a5d53c-fdc4-5271-b464-bb01b0283d87","task_revision_id":"1","upstream_id":"","short_description":"The graph of the function $f$ is shown below. How many solutions does the…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"The graph of the function $f$ is shown below. How many solutions does the equation $f(f(x))=6$ have?\\n\\n[asy] import graph; size(200); defaultpen(fontsize(10pt)+linewidth(.8pt)); dotfactor=4;  pair P1=(-7,-4), P2=(-2,6), P3=(0,0), P4=(1,6), P5=(5,-6); real[] xticks={-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6}; real[] yticks={-6,-5,-4,-3,-2,-1,1,2,3,4,5,6};  draw(P1--P2--P3--P4--P5);  dot(\\\"(-7, -4)\\\",P1); dot(\\\"(-2, 6)\\\",P2,LeftSide); dot(\\\"(1, 6)\\\",P4); dot(\\\"(5, -6)\\\",P5);  xaxis(\\\"$x$\\\",-7.5,7,Ticks(xticks),EndArrow(6)); yaxis(\\\"$y$\\\",-6.5,7,Ticks(yticks),EndArrow(6)); [/asy]\",\"type\":\"Intermediate Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}