{"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":"6f3cb83b-8dab-5f5e-826d-c47871169300","task_key":"intermediate~5falgebra--test--6f3cb83b-8dab-5f5e-826d-c47871169300","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 3\",\"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\\nWhich is the graph of $y = f(2x + 1)$?\\n\\n[asy]\\nunitsize(0.3 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 funca(real x) {\\n  return(func(2*x + 1));\\n}\\n\\nfor (n = 1; n <= 5; ++n) {\\n  graf[n] = new picture;\\n  for (i = -8; i <= 8; ++i) {\\n    draw(graf[n],(i,-8)--(i,8),gray(0.7));\\n    draw(graf[n],(-8,i)--(8,i),gray(0.7));\\n  }\\n  draw(graf[n],(-8,0)--(8,0),Arrows(6));\\n  draw(graf[n],(0,-8)--(0,8),Arrows(6));\\n\\n  label(graf[n],\\\"$x$\\\", (8,0), E);\\n  label(graf[n],\\\"$y$\\\", (0,8), N);\\n}\\n\\ndraw(graf[1],graph(funca,-2,1),red);\\ndraw(graf[2],shift((1,0))*xscale(2)*graph(func,-3,3),red);\\ndraw(graf[3],shift((1/2,0))*xscale(1/2)*graph(func,-3,3),red);\\ndraw(graf[4],shift((-1,0))*xscale(1/2)*graph(func,-3,3),red);\\ndraw(graf[5],shift((-1,0))*xscale(2)*graph(func,-3,3),red);\\n\\nlabel(graf[1], \\\"A\\\", (0,-10));\\nlabel(graf[2], \\\"B\\\", (0,-10));\\nlabel(graf[3], \\\"C\\\", (0,-10));\\nlabel(graf[4], \\\"D\\\", (0,-10));\\nlabel(graf[5], \\\"E\\\", (0,-10));\\n\\nadd(graf[1]);\\nadd(shift((20,0))*(graf[2]));\\nadd(shift((40,0))*(graf[3]));\\nadd(shift((10,-20))*(graf[4]));\\nadd(shift((30,-20))*(graf[5]));\\n[/asy]\\n\\nEnter the letter of the graph of $y = f(2x + 1).$\",\"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":[]}