{"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":"4257eb8e-2c07-5c50-814b-643abf6b3b1b","task_key":"intermediate~5falgebra--test--4257eb8e-2c07-5c50-814b-643abf6b3b1b","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 1\",\"problem\":\"The graph of $y = f(x)$ is shown below.\\n\\n[asy]\\nunitsize(0.5 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 = -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,-3,3),red);\\n\\nlabel(\\\"$y = f(x)$\\\", (3,-2), UnFill);\\n[/asy]\\n\\nWhich is the graph of $y = -f(x)$?\\n\\n[asy]\\nunitsize(0.5 cm);\\n\\npicture[] graf;\\nint i, n;\\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 funcb(real x) {\\n  return(-func(x));\\n}\\n\\nreal funcd(real x) {\\n  return(-func(-x));\\n}\\n\\nreal funce(real x) {\\n  return(func(-x));\\n}\\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],(-5,3)--(-2,0),red);\\ndraw(graf[1],arc((-2,2),2,270,360),red);\\ndraw(graf[1],(0,2)--(2,4),red);\\ndraw(graf[2],graph(funcb,-3,3),red);\\ndraw(graf[3],(-3,2)--(-2,0),red);\\ndraw(graf[3],arc((-2,-2),2,0,90),red);\\ndraw(graf[3],(0,-2)--(3,-5),red);\\ndraw(graf[4],graph(funcd,-3,3),red);\\ndraw(graf[5],graph(funce,-3,3),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 $y = -f(x).$\",\"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":[]}