{"id":"cb_question_bank:e0717857-0c6f-45e8-ae0f-d9b7c985a8a2","source_id":"cb_question_bank","source_item_id":"e0717857-0c6f-45e8-ae0f-d9b7c985a8a2","external_id":"87f878d4-305d-414f-8da8-f430f23c0bfd","ibn":null,"question_id":"9b5b23fc","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.D.","skill":"Two-variable data: Models and scatterplots","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"For x greater than 0 , the function f is defined as follows: f left parenthesis x right parenthesis equals 201 percent sign of x Which of the following could describe this function?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">For <math alttext=\"x greater than 0\"><mi>x</mi><mo>&gt;</mo><mn>0</mn></math>, the function <math alttext=\"f\"><mi>f</mi>\n</math> is defined as follows:</p>\n<p style=\"text-align: center;\"><math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>&nbsp;equals <math alttext=\"201 percent sign\"><mrow><mn>201</mn></mrow><mo>%</mo></math> of <math alttext=\"x\"><mi>x</mi>\n</math></p>\n<p style=\"text-align: left;\">Which of the following could describe this function?</p>","rationale_html":"<p style=\"text-align: left;\">Choice D is correct. It's given that for&nbsp;<math alttext=\"x greater than 0\"><mi>x</mi><mo>&gt;</mo><mn>0</mn></math>, <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> is equal to&nbsp;<math alttext=\"201 percent sign\"><mn>201</mn><mo>%</mo></math> of <math alttext=\"x\"><mi>x</mi>\n</math>. This is equivalent to&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals StartFraction 201 Over 100 EndFraction x\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mn>201</mn><mn>100</mn></mfrac><mi>x</mi></math>, or <math alttext=\"f left parenthesis x right parenthesis equals 2.01 x\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>2.01</mn><mi>x</mi></math>, for <math alttext=\"x greater than 0\"><mi>x</mi><mo>&gt;</mo><mn>0</mn></math>. This function indicates that as <math alttext=\"x\"><mi>x</mi>\n</math> increases,&nbsp;<math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> also increases, which means <math alttext=\"f\"><mi>f</mi>\n</math> is an increasing function. Furthermore,&nbsp; <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> increases at a constant rate of <math alttext=\"2.01\"><mn>2.01</mn>\n</math> for each increase of <math alttext=\"x\"><mi>x</mi>\n</math> by <math alttext=\"1\"><mn>1</mn>\n</math>. A function with a constant rate of change is linear. Thus, the function <math alttext=\"f\"><mi>f</mi>\n</math> can be described as an increasing linear function.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual errors.</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. This could describe the function <math alttext=\"f left parenthesis x right parenthesis equals left parenthesis 2.01 right parenthesis Superscript x\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mfenced><mn>2.01</mn></mfenced><mi>x</mi></msup></math>, where <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> is equal to&nbsp;<math alttext=\"201 percent sign\"><mn>201</mn><mo>%</mo></math> of&nbsp;<math alttext=\"f left parenthesis x minus 1 right parenthesis\"><mi>f</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math>, not <math alttext=\"x\"><mi>x</mi>\n</math>, for&nbsp;<math alttext=\"x greater than 0\"><mi>x</mi><mo>&gt;</mo><mn>0</mn></math>.</p>","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.834000+00:00","source_updated_at":"2023-08-02T20:25:59.834000+00:00","options":[{"label":"A","content_html":"<p style=\"text-align: left;\">Decreasing exponential</p>","ord":0},{"label":"B","content_html":"<p style=\"text-align: left;\">Decreasing linear</p>","ord":1},{"label":"C","content_html":"<p style=\"text-align: left;\">Increasing exponential</p>","ord":2},{"label":"D","content_html":"<p style=\"text-align: left;\">Increasing linear</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}}