{"id":"cb_question_bank:5e2e2219-f748-4943-9f30-70396e1fa439","source_id":"cb_question_bank","source_item_id":"5e2e2219-f748-4943-9f30-70396e1fa439","external_id":null,"ibn":"029475-DC","question_id":"c4cd5bcc","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the xy -plane, the y -coordinate of the y -intercept of the graph of the function f is c . Which of the following must be equal to c ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">In the <span class=\"italic \">xy</span>-plane, the <span class=\"italic \">y</span>-coordinate of the <span class=\"italic \">y</span>-intercept of the graph of the function <span class=\"italic\">f</span> is <span class=\"italic\">c</span>. Which of the following must be equal to <span class=\"italic\">c</span> ?</p>\n","rationale_html":"<p>Choice A is correct. A <span class=\"italic\">y</span>-intercept is the point in the <span class=\"italic\">xy</span>-plane where the graph of the function crosses the <span class=\"italic\">y</span>-axis, which is where <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/37b98ea685bc6992d8e8e7df92ac8c58c1621b437bc601cc6767a21168bc15e0\" alt=\"x equals 0\"></span>. It’s given that the <span class=\"italic\">y</span>-coordinate of the <span class=\"italic\">y</span>-intercept of the graph of function <span class=\"italic\">f</span> is <span class=\"italic\">c</span>. It follows that the coordinate pair representing the <span class=\"italic\">y</span>-intercept must be <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3a47727b67cf6370d95500541739a4a18e0f3c5928fad7c02257ac0b7a8ac833\" alt=\"the point with coordinates 0 comma c\"></span>. Therefore, <span class=\"italic\">c</span> must equal <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/71e4d225c23fa18669701f51868419bbefb60c3c262396a73b0a4220cd456bc2\" alt=\"f of 0\"></span>.</p><p>Choices B, C, and D are incorrect because <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e18f2dd72b8bae075ed41c099e7d195037939975d44bad1b46dd6a0371b05b3c\" alt=\"f of 1\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c534a5a7cf84ff0c1cd81dff96930fca311cecf67f58b25ebb4ae7baceba1574\" alt=\"f of 2\"></span>, and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2941316e5e47bc3a1dc8048bc5063aaa540fd944bb9266acea6b11614dabf6ef\" alt=\"f of 3\"></span>would represent the <span class=\"italic\">y</span>-value of the coordinate where <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6e4319fe2c5755fc5aa3f69e1a43b989d061cbb17c450f24b51a6616f131de4b\" alt=\"x equals 1\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/401169281090f4f1d9aafeeb928524e672d737cdce814b4e9256c5e06a42d325\" alt=\"x equals 2\"></span>, and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ceba1165e53a8baa1cf03f75cde85da34750b8ab2728ef25385d77f80f8276c5\" alt=\"x equals 3\"></span>, respectively.</p><p>&nbsp;</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.625000+00:00","source_updated_at":"2023-08-02T20:25:59.625000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/71e4d225c23fa18669701f51868419bbefb60c3c262396a73b0a4220cd456bc2\" alt=\"f of 0\"></span></span></p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e18f2dd72b8bae075ed41c099e7d195037939975d44bad1b46dd6a0371b05b3c\" alt=\"f of 1\"></span></span></p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c534a5a7cf84ff0c1cd81dff96930fca311cecf67f58b25ebb4ae7baceba1574\" alt=\"f of 2\"></span></span></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2941316e5e47bc3a1dc8048bc5063aaa540fd944bb9266acea6b11614dabf6ef\" alt=\"f of 3\"></span></span></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}}