{"id":"cb_question_bank:45194be8-db5a-4ff0-ae9a-08a92aed4cf2","source_id":"cb_question_bank","source_item_id":"45194be8-db5a-4ff0-ae9a-08a92aed4cf2","external_id":"f0bbaf49-87a8-4fb3-b54f-eadea2dca1a9","ibn":null,"question_id":"e470e19d","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The function f is defined by f left parenthesis x right parenthesis equals 7 x minus 84 . What is the x -intercept of the graph of y equals f left parenthesis x right parenthesis in the xy -plane?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The function <math alttext=\"f\"><mi>f</mi>\n</math> is defined by <math alttext=\"f left parenthesis x right parenthesis equals 7 x minus 84\"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mrow><mn>7</mn></mrow><mi>x</mi><mo>-</mo><mrow><mn>84</mn></mrow></math>. What is the <em>x</em>-intercept of the graph of <math alttext=\"y equals f left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> in the <em>xy</em>-plane?</p>","rationale_html":"<p style=\"text-align: left;\">Choice D is correct. The given function <math alttext=\"f\"><mi>f</mi></math> is a linear function. Therefore, the graph of <math alttext=\"y equals f left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> in the <em>xy</em>-plane has one <em>x</em>-intercept at the point <math alttext=\"left parenthesis k comma 0 right parenthesis\"><mfenced><mrow><mi>k</mi><mo>,</mo><mn>0</mn></mrow></mfenced></math>, where <math alttext=\"k\"><mi>k</mi>\n</math> is a constant. Substituting <math alttext=\"0\"><mn>0</mn>\n</math> for&nbsp;<math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> and <math alttext=\"k\"><mi>k</mi>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the given function yields <math alttext=\"0 equals 7 k minus 84\"><mn>0</mn><mo>=</mo><mn>7</mn><mi>k</mi><mo>-</mo><mn>84</mn></math>. Adding <math alttext=\"84\"><mn>84</mn>\n</math> to both sides of this equation yields <math alttext=\"84 equals 7 k\"><mn>84</mn><mo>=</mo><mn>7</mn><mi>k</mi></math>. Dividing both sides of this equation by <math alttext=\"7\"><mn>7</mn>\n</math> yields <math alttext=\"12 equals k\"><mn>12</mn><mo>=</mo><mi>k</mi></math>. Therefore, the <em>x</em>-intercept of the graph of&nbsp;<math alttext=\"y equals f left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> in the <em>xy</em>-plane&nbsp;is <math alttext=\"left parenthesis 12 comma 0 right parenthesis\"><mfenced><mrow><mn>12</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math>.</p>\n<p>Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice C is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.811000+00:00","source_updated_at":"2023-08-02T20:25:59.811000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"left parenthesis negative 12 comma 0 right parenthesis\"><mfenced><mrow><mrow><mo>-</mo><mn>12</mn></mrow><mo>,</mo><mn>0</mn></mrow></mfenced></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"left parenthesis negative 7 comma 0 right parenthesis\"><mfenced><mrow><mrow><mo>-</mo><mn>7</mn></mrow><mo>,</mo><mn>0</mn></mrow></mfenced></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"left parenthesis 7 comma 0 right parenthesis\"><mfenced><mrow><mrow><mn>7</mn></mrow><mo>,</mo><mn>0</mn></mrow></mfenced></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"left parenthesis 12 comma 0 right parenthesis\"><mfenced><mrow><mrow><mn>12</mn></mrow><mo>,</mo><mn>0</mn></mrow></mfenced></math></p>","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}}