{"id":"cb_question_bank:7321afbc-70e7-4bf5-8848-f2227608fd5a","source_id":"cb_question_bank","source_item_id":"7321afbc-70e7-4bf5-8848-f2227608fd5a","external_id":"79c4d360-5538-4b1d-992c-a822445814d8","ibn":null,"question_id":"a9039591","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":"x f left parenthesis x right parenthesis 0 29 1 32 2 35 For the linear function f , the table shows three values of x and their corresponding values of f left parenthesis x right parenthesis . Which equation defines f left parenthesis x right parenthesis ?","stimulus":"","stimulus_html":null,"stem_html":"<figure class=\"table\"><figure class=\"table\"><figure class=\"table\"><table border=\"1\">\n<thead>\n<tr>\n<th style=\"width: 47.2589%; text-align: center;\" scope=\"col\"><math alttext=\"x\"><mi>x</mi>\n</math></th>\n<th style=\"width: 47.2589%; text-align: center;\" scope=\"col\"><math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></th>\n</tr>\n</thead>\n<tbody>\n<tr>\n<td style=\"width: 47.2589%; text-align: center;\"><math alttext=\"0\"><mn>0</mn>\n</math></td>\n<td style=\"width: 47.2589%; text-align: center;\"><math alttext=\"29\"><mn>29</mn>\n</math></td>\n</tr>\n<tr>\n<td style=\"width: 47.2589%; text-align: center;\"><math alttext=\"1\"><mn>1</mn>\n</math></td>\n<td style=\"width: 47.2589%; text-align: center;\"><math alttext=\"32\"><mn>32</mn>\n</math></td>\n</tr>\n<tr>\n<td style=\"width: 47.2589%; text-align: center;\"><math alttext=\"2\"><mn>2</mn>\n</math></td>\n<td style=\"width: 47.2589%; text-align: center;\"><math alttext=\"35\"><mn>35</mn>\n</math></td>\n</tr>\n</tbody>\n</table></figure></figure></figure>\n<p style=\"text-align: left;\">For the linear function <math alttext=\"f\"><mi>f</mi>\n</math>, the table shows three values of <math alttext=\"x\"><mi>x</mi>\n</math> and their corresponding values of <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>. Which equation defines <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. An equation that defines a&nbsp;linear function <math alttext=\"f\"><mi>f</mi>\n</math> can be written in the form <math alttext=\"f left parenthesis x right parenthesis equals m x plus b\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>b</mi></math>, where <math alttext=\"m\"><mi>m</mi>\n</math> and <math alttext=\"b\"><mi>b</mi>\n</math> are constants. It's given in the table that when <math alttext=\"x equals 0\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math>, <math alttext=\"f left parenthesis x right parenthesis equals 29\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>29</mn></math>. Substituting <math alttext=\"0\"><mn>0</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> and <math alttext=\"29\"><mn>29</mn>\n</math> for&nbsp;<math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> in the equation&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals m x plus b\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>b</mi></math> yields&nbsp;<math alttext=\"29 equals m left parenthesis 0 right parenthesis plus b\"><mn>29</mn><mo>=</mo><mi>m</mi><mfenced><mn>0</mn></mfenced><mo>+</mo><mi>b</mi></math>, or <math alttext=\"29 equals b\"><mrow>\n\t<mn>29</mn>\n\t<mo>=</mo>\n\t<mi>b</mi>\n</mrow>\n</math>. Substituting <math alttext=\"29\"><mn>29</mn>\n</math> for <math alttext=\"b\"><mi>b</mi>\n</math> in the equation&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals m x plus b\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>b</mi></math> yields&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals m x plus 29\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mn>29</mn></math>. It's also given in the table that when <math alttext=\"x equals 1\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>1</mn>\n</mrow>\n</math>,&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals 32\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>32</mn></math>. Substituting <math alttext=\"1\"><mn>1</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> and <math alttext=\"32\"><mn>32</mn>\n</math> for&nbsp;<math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> in the equation&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals m x plus 29\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mn>29</mn></math> yields&nbsp;<math alttext=\"32 equals m left parenthesis 1 right parenthesis plus 29\"><mn>32</mn><mo>=</mo><mi>m</mi><mfenced><mn>1</mn></mfenced><mo>+</mo><mn>29</mn></math>, or <math alttext=\"32 equals m plus 29\"><mrow>\n\t<mn>32</mn>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mi>m</mi>\n\t\t<mo>+</mo>\n\t\t<mn>29</mn>\n\t</mrow>\n</mrow>\n</math>. Subtracting <math alttext=\"29\"><mn>29</mn>\n</math> from both sides of this equation yields <math alttext=\"3 equals m\"><mrow>\n\t<mn>3</mn>\n\t<mo>=</mo>\n\t<mi>m</mi>\n</mrow>\n</math>. Substituting <math alttext=\"3\"><mn>3</mn>\n</math> for <math alttext=\"m\"><mi>m</mi>\n</math> in the equation&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals m x plus 29\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mn>29</mn></math> yields <math alttext=\"f left parenthesis x right parenthesis equals 3 x plus 29\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>29</mn></math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":true,"source_created_at":"2023-08-02T20:25:59.812000+00:00","source_updated_at":"2023-08-02T20:25:59.812000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"f left parenthesis x right parenthesis equals 3 x plus 29\"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mrow>\n\t<mrow>\n\t\t<mn>3</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>29</mn>\n</mrow>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"f left parenthesis x right parenthesis equals 29 x plus 32\"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mrow>\n\t<mrow>\n\t\t<mn>29</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>32</mn>\n</mrow>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"f left parenthesis x right parenthesis equals 35 x plus 29\"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mrow>\n\t<mrow>\n\t\t<mn>35</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>29</mn>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"f left parenthesis x right parenthesis equals 32 x plus 35\"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mrow>\n\t<mrow>\n\t\t<mn>32</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>35</mn>\n</mrow>\n</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}}