{"id":"cb_question_bank:b107c165-1235-4465-bd7e-574cfeab5695","source_id":"cb_question_bank","source_item_id":"b107c165-1235-4465-bd7e-574cfeab5695","external_id":null,"ibn":"021441-DC","question_id":"d46da42c","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The function f is defined as shown. Which of the following graphs in the xy -plane could be the graph of y equals, f of x ?","stimulus":"f of x equals, x squared, plus 4","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dd9c0ca5156134c91bb58f31191ed269d8959ed2e8e46d3e5ed725707a095c63\" alt=\"f of x equals, x squared, plus 4\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">The function <span class=\"italic\">f</span> is defined as shown. Which of the following graphs in the <span class=\"italic \">xy</span>-plane could be the graph of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1e01733cd755d260e76d5f12c4cac64337f711b1e9607c6bccfbf87900f24efe\" alt=\"y equals, f of x\"></span> ?</p>\n","rationale_html":"<p>Choice D is correct. For the quadratic function <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dd9c0ca5156134c91bb58f31191ed269d8959ed2e8e46d3e5ed725707a095c63\" alt=\"f of x equals, x squared, plus 4\"></span>, the vertex of the graph is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d733af07db4a0ffb955944e977bb44a1ef279a092b1517e7acf09caf1a336c4f\" alt=\"the point with coordinates 0 comma 4\"></span>, and because the <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3a186314172bc239fb025135d8722d39ee39bfefe4e212836956158aa0b9ff08\" alt=\"x squared \"></span> term is positive, the vertex is the minimum of the function. Choice D is the only option that meets these conditions.</p><p>Choices A, B, and C are incorrect. The vertex of each of these graphs doesn’t correspond to the minimum of the given function.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.616000+00:00","source_updated_at":"2023-08-02T20:25:59.616000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"inline_image \">\n            </span>\n          </p><p>\n          <img src=\"/api/assets/85e76f73b096ceaef38b8f8d3c225283f38644f37713d841d97cf0d1f659e510\" alt=\"The answer choice presents the graph of a curve in the x y plane, with the origin labeled O. The numbers negative 8, negative 4, 4, and 8 are indicated on each axis. There are horizontal gridlines at the numbers negative 8 through 8, in increments of 2, on the y axis, and there are vertical gridlines at the numbers negative 8 through 8, in increments of 2, on the x axis. The figure presents an upward opening parabola, whose vertex lies at negative 4 on the y axis. The parabola crosses the x axis at negative 2 and 2.\" width=\"114\" height=\"118\"></p><p></p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"inline_image \">\n            </span>\n          </p><p>\n          <img src=\"/api/assets/178a93ab4a3fe485b0bea385ae29307fe0738b89b91ff394ed444b0b4b4fe86d\" alt=\"The answer choice presents the graph of a curve in the x y plane, with the origin labeled O. The numbers negative 8, negative 4, 4, and 8 are indicated on each axis. There are horizontal gridlines at the numbers negative 8 through 8, in increments of 2, on the y axis, and there are vertical gridlines at the numbers negative 8 through 8, in increments of 2, on the x axis. The figure presents an upward opening parabola, whose vertex lies at negative 4 on the x axis. The parabola passes through the point with coordinates negative 6 comma 4, and the point with coordinates negative 2 comma 4.\" width=\"114\" height=\"118\"></p><p></p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"inline_image \">\n            </span>\n          </p><p>\n          <img src=\"/api/assets/1b86890e182e299acebbd8caf3e1048a5c11963b6c6ab3d68e32bd42f9d5898c\" alt=\"The answer choice presents the graph of a curve in the x y plane, with the origin labeled O. The numbers negative 8, negative 4, 4, and 8 are indicated on each axis. There are horizontal gridlines at the numbers negative 8 through 8, in increments of 2, on the y axis, and there are vertical gridlines at the numbers negative 8 through 8, in increments of 2, on the x axis. The figure presents an upward opening parabola, whose vertex lies at 4 on the x axis. The parabola passes through the point with coordinates 2 comma 4, and the point with coordinates 6 comma 4.\" width=\"114\" height=\"118\"></p><p></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"inline_image \">\n            </span>\n          </p><p>\n          <img src=\"/api/assets/4de89aba3e26a1f3134ff2c08546e9c086fd1fbf1c05eae4bc8225bf91c12ff8\" alt=\"The answer choice presents the graph of a curve in the x y plane, with the origin labeled O. The numbers negative 8, negative 4, 4, and 8 are indicated on each axis. There are horizontal gridlines at the numbers negative 8 through 8, in increments of 2, on the y axis, and there are vertical gridlines at the numbers negative 8 through 8, in increments of 2, on the x axis. The figure presents an upward opening parabola, whose vertex lies at 4 on the y axis. The parabola passes through the point with coordinates negative 2 comma 8, and the point with coordinates 2 comma 8.\" width=\"114\" height=\"118\"></p><p></p>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}