{"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":"ed40fb38-6368-51ae-b9b7-18566eb06cc0","task_key":"intermediate~5falgebra--test--ed40fb38-6368-51ae-b9b7-18566eb06cc0","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 4\",\"problem\":\"The graph of $y = f(x)$ is shown below.\\n\\n[asy]\\nunitsize(0.3 cm);\\n\\nreal func(real x) {\\n  real y;\\n  if (x >= -3 && x <= 0) {y = -2 - x;}\\n  if (x >= 0 && x <= 2) {y = sqrt(4 - (x - 2)^2) - 2;}\\n  if (x >= 2 && x <= 3) {y = 2*(x - 2);}\\n  return(y);\\n}\\n\\nint i, n;\\n\\nfor (i = -8; i <= 8; ++i) {\\n  draw((i,-8)--(i,8),gray(0.7));\\n  draw((-8,i)--(8,i),gray(0.7));\\n}\\n\\ndraw((-8,0)--(8,0),Arrows(6));\\ndraw((0,-8)--(0,8),Arrows(6));\\n\\nlabel(\\\"$x$\\\", (8,0), E);\\nlabel(\\\"$y$\\\", (0,8), N);\\n\\ndraw(graph(func,-3,3),red);\\n\\nlabel(\\\"$y = f(x)$\\\", (4,-3), UnFill);\\n[/asy]\\n\\nThe graph of $y = g(x)$ is shown below.\\n\\n[asy]\\nunitsize(0.3 cm);\\n\\nreal func(real x) {\\n  real y;\\n  if (x >= -3 && x <= 0) {y = -2 - x;}\\n  if (x >= 0 && x <= 2) {y = sqrt(4 - (x - 2)^2) - 2;}\\n  if (x >= 2 && x <= 3) {y = 2*(x - 2);}\\n  return(y);\\n}\\n\\nreal gunc(real x) {\\n  return(3 - 2*func(x));\\n}\\n\\nint i, n;\\n\\nfor (i = -8; i <= 8; ++i) {\\n  draw((i,-8)--(i,8),gray(0.7));\\n  draw((-8,i)--(8,i),gray(0.7));\\n}\\n\\ndraw((-8,0)--(8,0),Arrows(6));\\ndraw((0,-8)--(0,8),Arrows(6));\\n\\nlabel(\\\"$x$\\\", (8,0), E);\\nlabel(\\\"$y$\\\", (0,8), N);\\n\\ndraw(graph(gunc,-3,3),red);\\n\\nlabel(\\\"$y = g(x)$\\\", (5,5), UnFill);\\n[/asy]\\n\\nWhat is $g(x)$ in terms of $f(x)$?  For example, if you think $g(x) = f(x) + 1,$ enter \\\"$f(x) + 1$\\\", without quotation marks.\",\"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":[]}