{"id":"cb_question_bank:6403aedc-b4d4-4c87-b7af-14bae56e6f9a","source_id":"cb_question_bank","source_item_id":"6403aedc-b4d4-4c87-b7af-14bae56e6f9a","external_id":null,"ibn":"027803-DC","question_id":"d675744f","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which of the following is the graph in the xy -plane of the given equation?","stimulus":"y equals, 4 times, open parenthesis, 2 to the x power, close parenthesis","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/61f2a469db3d319bf0ab72fcf8a560b9140342da30638d12cba19600af942257\" alt=\"y equals, 4 times, open parenthesis, 2 to the x power, close parenthesis\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">Which of the following is the graph in the <span class=\"italic \">xy</span>-plane of the given equation?</p>\n","rationale_html":"<p>Choice D is correct. The <span class=\"italic\">y</span>-intercept of the graph of an equation is the point <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9dd934c7a6127135240926c5f7629e6538b169f04d5b05cda606fb0a36f0fb9c\" alt=\"with coordinates 0 comma b\"></span>, where <span class=\"italic\">b</span> is the value of <span class=\"italic\">y</span> when <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/37b98ea685bc6992d8e8e7df92ac8c58c1621b437bc601cc6767a21168bc15e0\" alt=\"x equals 0\"></span>. For the given equation, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/365d9f5d9b81010454782b3469da46ef190dc0cfe2a2d209adba7c5a64556429\" alt=\"y equals 4 \"></span> when <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/37b98ea685bc6992d8e8e7df92ac8c58c1621b437bc601cc6767a21168bc15e0\" alt=\"x equals 0\"></span>. It follows that the <span class=\"italic\">y</span>-intercept of the graph of the given equation 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>. Additionally, for the given equation, the value of <span class=\"italic\">y</span> doubles for each increase of 1 in the value of <span class=\"italic\">x</span>. Therefore, the graph contains the points <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f521483f1978fa0b1ca05eb607caf7b1918730766f531a06fb64008aa1577f86\" alt=\"with coordinates 1 comma 8\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/db520bcfa07d47f9be8f31b8f3771a665213716fd9446c6a8f7711e36007484a\" alt=\"2 comma 16\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d7a6dec52851dcc6f88f08e402fef46b8ca79e17d818281ac135fbce706a51ce\" alt=\"3 comma 32\"></span>, and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6e7f87789ef9838f1ba2189ca491dddc0c59665c97cd479dbf88c8ce84b1dfe7\" alt=\"4 comma 64\"></span>. Only the graph shown in choice D passes through these points.</p><p>Choices A and B are incorrect because these are graphs of decreasing, not increasing, exponential functions. Choice C is incorrect because the value of <span class=\"italic\">y</span> increases by a growth factor greater than 2 for each increase of 1 in the value of <span class=\"italic\">x</span>.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.622000+00:00","source_updated_at":"2023-08-02T20:25:59.622000+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/d3339f8b19a83c2929ef82376f33100622f3b1464c11efde19ba1a285fcd7f9c\" alt=\"The answer choice presents the graph of a curve in the x y plane, with the origin labeled O. The numbers negative 4 through 4, in increments of 1, are indicated on the x axis. The numbers negative 25 through 100, in increments of 25, are indicated on the y axis. The curve begins to the left of the y axis, high above the x-axis. As it moves rightward it goes downward, at first steeply, then more and more slowly as it gets closer and closer to the x axis. Eventually it goes downward toward the x axis so slowly it is almost horizontal. The curve passes through the point with coordinates negative 2 comma 32, and the point with coordinates negative 1 comma 8, and crosses the y-axis a little above the origin. It ends to the right of the y-axis, just above the x-axis. \" width=\"165\" 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/f300e14a36241d499d4fca1cab92ceccb286e4d49adc557227ca606cf923c1d6\" alt=\"The answer choice presents the graph of a curve in the x y plane, with the origin labeled O. The numbers negative 4 through 4, in increments of 1, are indicated on the x axis. The numbers negative 25 through 100, in increments of 25, are indicated on the y axis. The curve begins to the left of the y axis, high above the x axis. As it moves rightward it goes downward, at first steeply, then more and more slowly as it gets closer and closer to the x axis. Eventually it goes downward toward the x axis so slowly it is almost horizontal. It ends to the right of the y axis, just above the x axis. The curve passes through the point with coordinates negative 3 comma 32, the point with coordinates negative 2 comma 16, and the point with coordinates negative 1 comma 8. It crosses the y-axis a little above the origin and ends to the right of the y-axis, just above the x-axis.\" width=\"165\" 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/c5970c2fb1c752b42fc44bb14320bf2168b95baefcfdd55eccbc5a565fd279d5\" alt=\"The answer choice presents the graph of a curve in the x y plane, with the origin labeled O. The numbers negative 4 through 4, in increments of 1, are indicated on the x axis. The numbers negative 25 through 100, in increments of 25, are indicated on the y axis. The curve begins to the left of the y axis, just above the x axis. As it moves rightward, it goes upward, at first so slowly it is almost horizontal, then more and more quickly. The curve crosses the y-axis a little above the origin, and passes through the point with coordinates 1 comma 8 and the point with coordinates 2 comma 32. It ends to the right of the y-axis, high above the x-axis.\" width=\"165\" 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/2467a25bbed0e262e007cdf6f2442ca69c4e6ad553c81b0b7d2e705f5005bb9d\" alt=\"The answer choice presents the graph of a curve in the x y plane, with the origin labeled O. The numbers negative 4 through 4, in increments of 1, are indicated on the x axis. The numbers negative 25 through 100, in increments of 25, are indicated on the y axis. The curve begins to the left of the y axis, just above the x axis. As it moves rightward, it goes upward, at first so slowly it is almost horizontal, then more and more quickly. It ends to the right of the y axis, high above the x axis. The curve crosses the y axis a little above the origin, and it passes through the point with coordinates 1 comma 8, the point with coordinates 2 comma 16, and the point with coordinates 3 comma 32. It ends to the right of the y-axis, high above the x-axis.\" width=\"165\" 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}}