{"id":"cb_question_bank:6b5a9b3d-c52e-48f4-aec0-353d56e74af4","source_id":"cb_question_bank","source_item_id":"6b5a9b3d-c52e-48f4-aec0-353d56e74af4","external_id":"969792b2-4ab7-4fe4-8d9e-e1a709101015","ibn":null,"question_id":"67f4b449","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":"The function f left parenthesis w right parenthesis equals 6 w squared gives the area of a rectangle, in square feet left parenthesis ft squared right parenthesis , if its width is w ft and its length is 6 times its width. Which of the following is the best interpretation of f left parenthesis 14 right parenthesis equals 1,176 ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The function <math alttext=\"f left parenthesis w right parenthesis equals 6 w squared\"><mi>f</mi><mfenced><mi>w</mi></mfenced><mo>=</mo><mrow><mn>6</mn></mrow><msup><mi>w</mi><mn>2</mn></msup></math> gives the area of a rectangle, <math alttext=\"in square feet left parenthesis ft squared right parenthesis\"><mtext>in</mtext><mo>&nbsp;</mo><mtext>square</mtext><mo>&nbsp;</mo><mtext>feet</mtext><mo>&nbsp;</mo><mfenced><msup><mtext>ft</mtext><mn>2</mn></msup></mfenced></math>, if its width is <math alttext=\"w ft\"><mi>w</mi><mo>&nbsp;</mo><mtext>ft</mtext></math> and its length is <math alttext=\"6\"><mn>6</mn>\n</math> times its width. Which of the following is the best interpretation of <math alttext=\"f left parenthesis 14 right parenthesis equals 1,176\"><mi>f</mi><mfenced><mrow><mn>14</mn></mrow></mfenced><mo>=</mo><mn>1,176</mn>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. The function <math alttext=\"f\"><mi>f</mi>\n</math> gives the area of the rectangle, in <math alttext=\"ft Superscript 2\"><msup><mtext>ft</mtext><mn>2</mn></msup></math>, if its width is <math alttext=\"w ft\"><mi>w</mi><mo>&nbsp;</mo><mtext>ft</mtext></math>. Since the value of <math alttext=\"f left parenthesis 14 right parenthesis\"><mi>f</mi><mfenced><mn>14</mn></mfenced></math> is the value of <math alttext=\"f left parenthesis w right parenthesis\"><mi>f</mi><mfenced><mi>w</mi></mfenced></math> if <math alttext=\"w equals 14\"><mrow>\n\t<mi>w</mi>\n\t<mo>=</mo>\n\t<mn>14</mn>\n</mrow>\n</math>, it follows that&nbsp;<math alttext=\"f left parenthesis 14 right parenthesis equals 1,176\"><mi>f</mi><mfenced><mn>14</mn></mfenced><mo>=</mo><mn>1,176</mn></math> means that <math alttext=\"f left parenthesis w right parenthesis\"><mi>f</mi><mfenced><mi>w</mi></mfenced></math> is&nbsp;<math alttext=\"1,176\"><mn>1,176</mn></math> if <math alttext=\"w equals 14\"><mrow>\n\t<mi>w</mi>\n\t<mo>=</mo>\n\t<mn>14</mn>\n</mrow>\n</math>. In the given context, this means that if the width of the rectangle is <math alttext=\"14 ft\"><mn>14</mn><mo>&nbsp;</mo><mtext>ft</mtext></math>, then the area of the rectangle is <math alttext=\"1,176 ft squared\"><mn>1,176</mn><mo>&nbsp;</mo><msup><mtext>ft</mtext><mn>2</mn></msup></math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from interpreting <math alttext=\"f left parenthesis w right parenthesis\"><mi>f</mi><mfenced><mi>w</mi></mfenced></math> as the width, in <math alttext=\"ft\"><mtext>ft</mtext></math>, of the rectangle if its area is <math alttext=\"w ft squared\"><mi>w</mi><mo>&nbsp;</mo><msup><mtext>ft</mtext><mn>2</mn></msup></math>, rather than as the area, in <math alttext=\"ft Superscript 2\"><msup><mtext>ft</mtext><mn>2</mn></msup></math>, of the rectangle if its width is <math alttext=\"w ft\"><mi>w</mi><mo>&nbsp;</mo><mtext>ft</mtext></math>.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.825000+00:00","source_updated_at":"2023-08-02T20:25:59.825000+00:00","options":[{"label":"A","content_html":"<p style=\"text-align: left;\">If the width of the rectangle is <math alttext=\"14 ft\"><mrow><mn>14</mn></mrow><mo>&nbsp;</mo><mtext>ft</mtext></math>, then the area of the rectangle is <math alttext=\"1,176 ft squared\"><mrow><mn>1,176</mn></mrow><mo>&nbsp;</mo><msup><mtext>ft</mtext><mn>2</mn></msup></math>.</p>","ord":0},{"label":"B","content_html":"<p style=\"text-align: left;\">If the width of the rectangle is <math alttext=\"14 ft\"><mrow><mn>14</mn></mrow><mo>&nbsp;</mo><mtext>ft</mtext></math>, then the length of the rectangle is <math alttext=\"1,176 ft\"><mrow><mn>1,176</mn></mrow><mo>&nbsp;</mo><mtext>ft</mtext></math>.</p>","ord":1},{"label":"C","content_html":"<p style=\"text-align: left;\">If the width of the rectangle is <math alttext=\"1,176 ft\"><mrow><mn>1,176</mn></mrow><mo>&nbsp;</mo><mtext>ft</mtext></math>, then the length of the rectangle is <math alttext=\"14 ft\"><mrow><mn>14</mn></mrow><mo>&nbsp;</mo><mtext>ft</mtext></math>.</p>","ord":2},{"label":"D","content_html":"<p style=\"text-align: left;\">If the width of the rectangle is <math alttext=\"1,176 ft\"><mrow><mn>1,176</mn></mrow><mo>&nbsp;</mo><mtext>ft</mtext></math>, then the area of the rectangle is <math alttext=\"14 ft squared\"><mrow><mn>14</mn></mrow><mo>&nbsp;</mo><msup><mtext>ft</mtext><mn>2</mn></msup></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}}