{"id":"cb_question_bank:b6b43523-fbe7-494b-bd6c-d44c1dd682af","source_id":"cb_question_bank","source_item_id":"b6b43523-fbe7-494b-bd6c-d44c1dd682af","external_id":"73405bf8-4af6-4fad-9344-e38505f18416","ibn":null,"question_id":"45df91ee","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":"g left parenthesis x right parenthesis equals 11 left parenthesis one twelfth right parenthesis Superscript x If the given function g is graphed in the xy -plane, where y equals g left parenthesis x right parenthesis , what is the y -intercept of the graph?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"g left parenthesis x right parenthesis equals 11 left parenthesis one twelfth right parenthesis Superscript x\"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mrow><mn>11</mn></mrow><msup>\n\t<mfenced>\n\t\t<mfrac>\n\t\t\t<mn>1</mn>\n\t\t\t<mn>12</mn>\n\t\t</mfrac>\n\t</mfenced>\n\t<mi>x</mi>\n</msup>\n</math></p>\n<p style=\"text-align: left;\">If the given function <math alttext=\"g\"><mi>g</mi>\n</math> is graphed in the <em>xy</em>-plane, where <math alttext=\"y equals g left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>g</mi><mfenced><mi>x</mi></mfenced></math>, what is the <em>y</em>-intercept of the graph?</p>","rationale_html":"<p>Choice A is correct. The <em>x</em>-coordinate of any <em>y</em>-intercept of a graph is <math alttext=\"0\"><mn>0</mn>\n</math>. Substituting <math alttext=\"0\"><mn>0</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the given equation yields <math alttext=\"g left parenthesis 0 right parenthesis equals 11 left parenthesis one twelfth right parenthesis Superscript 0\"><mi>g</mi><mfenced><mn>0</mn></mfenced><mo>=</mo><mn>11</mn><msup><mfenced><mfrac><mn>1</mn><mn>12</mn></mfrac></mfenced><mn>0</mn></msup></math>. Since any nonzero number raised to the <math alttext=\"0 th\"><mn>0</mn><mtext>th</mtext></math> power is <math alttext=\"1\"><mn>1</mn>\n</math>, this gives <math alttext=\"g left parenthesis 0 right parenthesis equals 11 dot 1\"><mi>g</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>11</mn><mo>·</mo><mn>1</mn></math>, or <math alttext=\"g left parenthesis 0 right parenthesis equals 11\"><mi>g</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>11</mn></math>. The <em>y</em>-intercept of the graph is, therefore, the point <math alttext=\"left parenthesis 0 comma 11 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>11</mn></mrow></mfenced></math>.</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>\n<p>Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.828000+00:00","source_updated_at":"2023-08-02T20:25:59.828000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"left parenthesis 0 comma 11 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mrow><mn>11</mn></mrow></mrow></mfenced></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"left parenthesis 0 comma 132 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mrow><mn>132</mn></mrow></mrow></mfenced></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"left parenthesis 0 comma 1 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mrow><mn>1</mn></mrow></mrow></mfenced></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"left parenthesis 0 comma 12 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mrow><mn>12</mn></mrow></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}}