{"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":"a5aad767-b703-5e9e-ac6d-9304296df4b0","task_key":"intermediate~5falgebra--test--a5aad767-b703-5e9e-ac6d-9304296df4b0","task_revision_id":"1","upstream_id":"","short_description":"The graph of $y = f(x)$ is shown below.","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 2\",\"problem\":\"The graph of $y = f(x)$ is shown below.\\n\\n[asy]\\nunitsize(0.5 cm);\\n\\nreal func(real x) {\\n  return (log(x));\\n}\\n\\nint i, n;\\n\\nfor (i = -5; i <= 5; ++i) {\\n  draw((i,-5)--(i,5),gray(0.7));\\n  draw((-5,i)--(5,i),gray(0.7));\\n}\\n\\ndraw((-5,0)--(5,0),Arrows(6));\\ndraw((0,-5)--(0,5),Arrows(6));\\n\\nlabel(\\\"$x$\\\", (5,0), E);\\nlabel(\\\"$y$\\\", (0,5), N);\\n\\ndraw(graph(func,exp(-5),5),red);\\n\\nlabel(\\\"$y = f(x)$\\\", (3,-2), UnFill);\\n[/asy]\\n\\nWhich is the graph of $y = f^{-1}(x)$?\\n\\n[asy]\\nunitsize(0.5 cm);\\n\\npicture[] graf;\\nint i, n;\\n\\nreal func(real x) {\\n  return (log(x));\\n}\\n\\npath foo = graph(func,exp(-5),5); \\n\\nfor (n = 1; n <= 5; ++n) {\\n  graf[n] = new picture;\\n  for (i = -5; i <= 5; ++i) {\\n    draw(graf[n],(i,-5)--(i,5),gray(0.7));\\n    draw(graf[n],(-5,i)--(5,i),gray(0.7));\\n  }\\n  draw(graf[n],(-5,0)--(5,0),Arrows(6));\\n  draw(graf[n],(0,-5)--(0,5),Arrows(6));\\n\\n  label(graf[n],\\\"$x$\\\", (5,0), E);\\n  label(graf[n],\\\"$y$\\\", (0,5), N);\\n}\\n\\ndraw(graf[1],reflect((0,0),(0,1))*foo,red);\\ndraw(graf[2],reflect((0,0),(1,-1))*foo,red);\\ndraw(graf[3],reflect((0,0),(1,0))*foo,red);\\ndraw(graf[4],rotate(180)*foo,red);\\ndraw(graf[5],reflect((0,0),(1,1))*foo,red);\\n\\nlabel(graf[1], \\\"A\\\", (0,-6));\\nlabel(graf[2], \\\"B\\\", (0,-6));\\nlabel(graf[3], \\\"C\\\", (0,-6));\\nlabel(graf[4], \\\"D\\\", (0,-6));\\nlabel(graf[5], \\\"E\\\", (0,-6));\\n\\nadd(graf[1]);\\nadd(shift((12,0))*(graf[2]));\\nadd(shift((24,0))*(graf[3]));\\nadd(shift((6,-12))*(graf[4]));\\nadd(shift((18,-12))*(graf[5]));\\n[/asy]\\n\\nEnter the letter of the graph of $y = f^{-1}(x).$\",\"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":[]}