{"id":"cb_question_bank:49363232-aa8c-4254-b2d3-a5bdeb17ef81","source_id":"cb_question_bank","source_item_id":"49363232-aa8c-4254-b2d3-a5bdeb17ef81","external_id":"e3e1bd01-4a4e-4c9c-8e91-28a5165667b6","ibn":null,"question_id":"50e40f08","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"M","score_band":4,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"f left parenthesis x right parenthesis equals left parenthesis x plus 6 right parenthesis left parenthesis x minus 4 right parenthesis If the given function f is graphed in the xy -plane, where y equals f left parenthesis x right parenthesis , what is the x -coordinate of an x -intercept of the graph?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"f left parenthesis x right parenthesis equals left parenthesis x plus 6 right parenthesis left parenthesis x minus 4 right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mrow><mn>6</mn></mrow></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>-</mo><mrow><mn>4</mn></mrow></mrow></mfenced></math></p>\n<p style=\"text-align: left;\">If the given function <math alttext=\"f\"><mi>f</mi>\n</math> is graphed in the <em>xy</em>-plane, where <math alttext=\"y equals f left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math>, what is the <em>x</em>-coordinate of an <em>x</em>-intercept of the graph?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is either <math alttext=\"negative 6\"><mo>-</mo><mn>6</mn>\n</math> or <math alttext=\"4\"><mn>4</mn>\n</math>. The <em>x</em>-intercepts of a graph in the <em>xy</em>-plane are the points where <math alttext=\"y equals 0\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math>. Thus, for an <em>x</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>, <math alttext=\"0 equals f left parenthesis x right parenthesis\"><mn>0</mn><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math>. Substituting <math alttext=\"0\"><mn>0</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 left parenthesis x plus 6 right parenthesis left parenthesis x minus 4 right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced></math> yields <math alttext=\"0 equals left parenthesis x plus 6 right parenthesis left parenthesis x minus 4 right parenthesis\"><mn>0</mn><mo>=</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced></math>. By the zero product property, <math alttext=\"x plus 6 equals 0\"><mrow>\n\t<mrow>\n\t\t<mi>x</mi>\n\t\t<mo>+</mo>\n\t\t<mn>6</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math> and <math alttext=\"x minus 4 equals 0\"><mrow>\n\t<mrow>\n\t\t<mi>x</mi>\n\t\t<mo>-</mo>\n\t\t<mn>4</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math>. Subtracting <math alttext=\"6\"><mn>6</mn>\n</math> from both sides of the equation <math alttext=\"x plus 6 equals 0\"><mrow>\n\t<mrow>\n\t\t<mi>x</mi>\n\t\t<mo>+</mo>\n\t\t<mn>6</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math> yields <math alttext=\"x equals negative 6\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mo>-</mo><mn>6</mn>\n</mrow>\n</math>. Adding <math alttext=\"4\"><mn>4</mn>\n</math> to both sides of the equation <math alttext=\"x minus 4 equals 0\"><mrow>\n\t<mrow>\n\t\t<mi>x</mi>\n\t\t<mo>-</mo>\n\t\t<mn>4</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math> yields <math alttext=\"x equals 4\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>4</mn>\n</mrow>\n</math>. Therefore, the <em>x</em>-coordinates of the <em>x</em>-intercepts 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> are <math alttext=\"negative 6\"><mo>-</mo><mn>6</mn>\n</math> and <math alttext=\"4\"><mn>4</mn>\n</math>. Note that -6 and 4 are examples of ways to enter a correct answer.</p>","correct_answer":["-6","4"],"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":[],"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}}