{"id":"cb_question_bank:b9958639-b0a1-4128-a8a9-4011cf516231","source_id":"cb_question_bank","source_item_id":"b9958639-b0a1-4128-a8a9-4011cf516231","external_id":"b4142eb8-7a46-4f1d-a34d-495ec7fb5693","ibn":null,"question_id":"aad7e1b9","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear 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 by f left parenthesis x right parenthesis equals one tenth x minus 2 . What is the y -intercept of the graph of y equals f left parenthesis x right parenthesis in the xy -plane?","stimulus":"","stimulus_html":null,"stem_html":"<p>The function <math alttext=\"f\"><mi>f</mi>\n</math><em> </em>is defined by <math alttext=\"f left parenthesis x right parenthesis equals one tenth x minus 2\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mn>1</mn><mrow><mn>10</mn></mrow></mfrac><mi>x</mi><mo>-</mo><mrow><mn>2</mn></mrow></math>. What is the <em>y</em>-intercept of 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?</p>","rationale_html":"<p>Choice B is correct. The <em>y</em>-intercept of the graph of a function in the <em>xy</em>-plane is the point on the graph where <math alttext=\"x equals 0\"><mi>x</mi><mo>=</mo><mn>0</mn></math>. It′s given that <math alttext=\"f left parenthesis x right parenthesis equals one tenth x minus 2\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mn>1</mn><mn>10</mn></mfrac><mi>x</mi><mo>-</mo><mn>2</mn></math>. Substituting <math alttext=\"0\"><mn>0</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in this equation yields <math alttext=\"f left parenthesis 0 right parenthesis equals one tenth left parenthesis 0 right parenthesis minus 2\"><mi>f</mi><mfenced><mn>0</mn></mfenced><mo>=</mo><mfrac><mn>1</mn><mn>10</mn></mfrac><mfenced><mn>0</mn></mfenced><mo>-</mo><mn>2</mn></math>, or <math alttext=\"f left parenthesis 0 right parenthesis equals negative 2\"><mi>f</mi><mfenced><mn>0</mn></mfenced><mo>=</mo><mo>-</mo><mn>2</mn></math>. Since it′s given that <math alttext=\"y equals f left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math>, it follows that <math alttext=\"y equals negative 2\"><mi>y</mi><mo>=</mo><mo>-</mo><mn>2</mn></math> when <math alttext=\"x equals 0\"><mi>x</mi><mo>=</mo><mn>0</mn></math>. Therefore, the <em>y</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 is&nbsp;<math alttext=\"left parenthesis 0 comma negative 2 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mo>-</mo><mn>2</mn></mrow></mfenced></math>.</p>\n<p>Choice A 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>\n<p>Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["B"],"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 2 comma 0 right parenthesis\"><mfenced><mrow><mrow><mo>-</mo><mn>2</mn></mrow><mo>,</mo><mn>0</mn></mrow></mfenced></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"left parenthesis 0 comma negative 2 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mrow><mo>-</mo><mn>2</mn></mrow></mrow></mfenced></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"left parenthesis 0 comma one tenth right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mfrac><mn>1</mn><mrow><mn>10</mn></mrow></mfrac></mrow></mfenced></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"left parenthesis one tenth comma 0 right parenthesis\"><mfenced><mrow><mfrac><mn>1</mn><mrow><mn>10</mn></mrow></mfrac><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}}