{"id":"cb_question_bank:ead95c1c-ad49-48ec-9ce4-73a466bb5be3","source_id":"cb_question_bank","source_item_id":"ead95c1c-ad49-48ec-9ce4-73a466bb5be3","external_id":"4e837070-2e7d-4f56-993a-9d8d616e345b","ibn":null,"question_id":"044c1cb7","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"h left parenthesis x right parenthesis equals x squared minus 3 Which table gives three values of x and their corresponding values of h left parenthesis x right parenthesis for the given function h ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"h left parenthesis x right parenthesis equals x squared minus 3\"><mi>h</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mrow><mn>3</mn></mrow></math></p>\n<p>Which table gives three values of <math alttext=\"x\"><mi>x</mi>\n</math> and their corresponding values of <math alttext=\"h left parenthesis x right parenthesis\"><mi>h</mi><mfenced><mi>x</mi></mfenced></math> for the given function <math alttext=\"h\"><mi>h</mi>\n</math>?</p>","rationale_html":"<p>Choice B is correct. It′s given that <math alttext=\"h left parenthesis x right parenthesis equals x squared minus 3\"><mi>h</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn></math>. Each table gives <math alttext=\"1\"><mn>1</mn>\n</math>, <math alttext=\"2\"><mn>2</mn>\n</math>, and <math alttext=\"3\"><mn>3</mn>\n</math> as the three given values of <math alttext=\"x\"><mi>x</mi>\n</math>. Substituting <math alttext=\"1\"><mn>1</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the equation&nbsp;<math alttext=\"h left parenthesis x right parenthesis equals x squared minus 3\"><mi>h</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn></math> yields <math alttext=\"h left parenthesis 1 right parenthesis equals left parenthesis 1 right parenthesis squared minus 3\"><mi>h</mi><mfenced><mn>1</mn></mfenced><mo>=</mo><msup><mfenced><mn>1</mn></mfenced><mn>2</mn></msup><mo>-</mo><mn>3</mn></math>, or <math alttext=\"h left parenthesis 1 right parenthesis equals negative 2\"><mi>h</mi><mfenced><mn>1</mn></mfenced><mo>=</mo><mo>-</mo><mn>2</mn></math>. Substituting <math alttext=\"2\"><mn>2</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the equation&nbsp;<math alttext=\"h left parenthesis x right parenthesis equals x squared minus 3\"><mi>h</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn></math> yields <math alttext=\"h left parenthesis 2 right parenthesis equals left parenthesis 2 right parenthesis squared minus 3\"><mi>h</mi><mfenced><mn>2</mn></mfenced><mo>=</mo><msup><mfenced><mn>2</mn></mfenced><mn>2</mn></msup><mo>-</mo><mn>3</mn></math>, or <math alttext=\"h left parenthesis 2 right parenthesis equals 1\"><mi>h</mi><mfenced><mn>2</mn></mfenced><mo>=</mo><mn>1</mn></math>. Finally, substituting <math alttext=\"3\"><mn>3</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the equation <math alttext=\"h left parenthesis x right parenthesis equals x squared minus 3\"><mi>h</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn></math> yields <math alttext=\"h left parenthesis 3 right parenthesis equals left parenthesis 3 right parenthesis squared minus 3\"><mi>h</mi><mfenced><mn>3</mn></mfenced><mo>=</mo><msup><mfenced><mn>3</mn></mfenced><mn>2</mn></msup><mo>-</mo><mn>3</mn></math>, or <math alttext=\"h left parenthesis 3 right parenthesis equals 6\"><mi>h</mi><mfenced><mn>3</mn></mfenced><mo>=</mo><mn>6</mn></math>. Therefore, <math alttext=\"h left parenthesis x right parenthesis\"><mi>h</mi><mfenced><mi>x</mi></mfenced></math> is&nbsp;<math alttext=\"negative 2\"><mo>-</mo><mn>2</mn></math> when <math alttext=\"x\"><mi>x</mi>\n</math> is <math alttext=\"1\"><mn>1</mn>\n</math>, <math alttext=\"h left parenthesis x right parenthesis\"><mi>h</mi><mfenced><mi>x</mi></mfenced></math> is <math alttext=\"1\"><mn>1</mn>\n</math> when <math alttext=\"x\"><mi>x</mi>\n</math> is <math alttext=\"2\"><mn>2</mn>\n</math>, and <math alttext=\"h left parenthesis x right parenthesis\"><mi>h</mi><mfenced><mi>x</mi></mfenced></math> is <math alttext=\"6\"><mn>6</mn>\n</math> when <math alttext=\"x\"><mi>x</mi>\n</math> is <math alttext=\"3\"><mn>3</mn>\n</math>. Choice B is a table with these values of <math alttext=\"x\"><mi>x</mi>\n</math> and their corresponding values of <math alttext=\"h left parenthesis x right parenthesis\"><mi>h</mi><mfenced><mi>x</mi></mfenced></math>.</p>\n<p>Choice A is incorrect. This is a table of values for the function <math alttext=\"h left parenthesis x right parenthesis equals x plus 3\"><mi>h</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>x</mi><mo>+</mo><mn>3</mn></math>, not <math alttext=\"h left parenthesis x right parenthesis equals x squared minus 3\"><mi>h</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn></math>.</p>\n<p>Choice C is incorrect. This is a table of values for the function <math alttext=\"h left parenthesis x right parenthesis equals 2 x minus 3\"><mi>h</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>2</mn><mi>x</mi><mo>-</mo><mn>3</mn></math>, not <math alttext=\"h left parenthesis x right parenthesis equals x squared minus 3\"><mi>h</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn></math>.</p>\n<p>Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":true,"source_created_at":"2023-08-02T20:25:59.827000+00:00","source_updated_at":"2023-08-02T20:25:59.827000+00:00","options":[{"label":"A","content_html":"<figure class=\"table left-justified\"><figure class=\"table left-justified\"><table border=\"1\">\n<tbody>\n<tr style=\"height: 22.3958px;\">\n<th style=\"width: 57.3264px;\" scope=\"row\" id=\"ea1f7b63-aa58-4342-aca9-c222fba8b559_option_1_tableColumn_1\"><math alttext=\"x\"><mi>x</mi>\n</math></th>\n<td style=\"width: 46.4931px;\" id=\"ea1f7b63-aa58-4342-aca9-c222fba8b559_option_1_tableColumn_2\"><math alttext=\"1\"><mn>1</mn>\n</math></td>\n<td style=\"width: 33.4722px;\" id=\"ea1f7b63-aa58-4342-aca9-c222fba8b559_option_1_tableColumn_3\"><math alttext=\"2\"><mn>2</mn>\n</math></td>\n<td style=\"width: 33.4722px;\" id=\"ea1f7b63-aa58-4342-aca9-c222fba8b559_option_1_tableColumn_4\"><math alttext=\"3\"><mn>3</mn>\n</math></td>\n</tr>\n<tr style=\"height: 22.3958px;\">\n<th style=\"\" scope=\"row\"><math alttext=\"h left parenthesis x right parenthesis\"><mi>h</mi><mfenced><mi>x</mi></mfenced></math></th>\n<td style=\"\"><math alttext=\"4\"><mn>4</mn>\n</math></td>\n<td style=\"\"><math alttext=\"5\"><mn>5</mn>\n</math></td>\n<td style=\"\"><math alttext=\"6\"><mn>6</mn>\n</math></td>\n</tr>\n</tbody>\n</table></figure></figure>","ord":0},{"label":"B","content_html":"<figure class=\"table left-justified\"><figure class=\"table left-justified\"><table border=\"1\">\n<tbody>\n<tr>\n<th style=\"text-align: center;  width: 57.3264px;\" scope=\"row\" id=\"543a7917-e484-48d8-acef-7612c9c40bd0_option_2_tableColumn_1\"><math alttext=\"x\"><mi>x</mi>\n</math></th>\n<td style=\"text-align: center;  width: 46.4931px;\" id=\"543a7917-e484-48d8-acef-7612c9c40bd0_option_2_tableColumn_2\"><math alttext=\"1\"><mn>1</mn>\n</math></td>\n<td style=\"text-align: center;  width: 33.4722px;\" id=\"543a7917-e484-48d8-acef-7612c9c40bd0_option_2_tableColumn_3\"><math alttext=\"2\"><mn>2</mn>\n</math></td>\n<td style=\"text-align: center;  width: 33.4722px;\" id=\"543a7917-e484-48d8-acef-7612c9c40bd0_option_2_tableColumn_4\"><math alttext=\"3\"><mn>3</mn>\n</math></td>\n</tr>\n<tr>\n<th style=\" text-align: center;\" scope=\"row\"><math alttext=\"h left parenthesis x right parenthesis\"><mi>h</mi><mfenced><mi>x</mi></mfenced></math></th>\n<td style=\" text-align: center;\"><math alttext=\"negative 2\"><mo>-</mo><mn>2</mn>\n</math></td>\n<td style=\" text-align: center;\"><math alttext=\"1\"><mn>1</mn>\n</math></td>\n<td style=\" text-align: center;\"><math alttext=\"6\"><mn>6</mn>\n</math></td>\n</tr>\n</tbody>\n</table></figure></figure>","ord":1},{"label":"C","content_html":"<figure class=\"table left-justified\"><figure class=\"table left-justified\"><table border=\"1\">\n<tbody>\n<tr style=\"height: 22.3958px;\">\n<th style=\"width: 57.3264px;\" scope=\"row\" id=\"11f000ec-04e1-4e0b-98ca-de7c4c759b60_option_3_tableColumn_1\"><math alttext=\"x\"><mi>x</mi>\n</math></th>\n<td style=\"width: 46.4931px;\" id=\"11f000ec-04e1-4e0b-98ca-de7c4c759b60_option_3_tableColumn_2\"><math alttext=\"1\"><mn>1</mn>\n</math></td>\n<td style=\"width: 33.4722px;\" id=\"11f000ec-04e1-4e0b-98ca-de7c4c759b60_option_3_tableColumn_3\"><math alttext=\"2\"><mn>2</mn>\n</math></td>\n<td style=\"width: 33.4722px;\" id=\"11f000ec-04e1-4e0b-98ca-de7c4c759b60_option_3_tableColumn_4\"><math alttext=\"3\"><mn>3</mn>\n</math></td>\n</tr>\n<tr style=\"height: 22.3958px;\">\n<th style=\"\" scope=\"row\"><math alttext=\"h left parenthesis x right parenthesis\"><mi>h</mi><mfenced><mi>x</mi></mfenced></math></th>\n<td style=\"\"><math alttext=\"negative 1\"><mo>-</mo><mn>1</mn>\n</math></td>\n<td style=\"\"><math alttext=\"1\"><mn>1</mn>\n</math></td>\n<td style=\"\"><math alttext=\"3\"><mn>3</mn>\n</math></td>\n</tr>\n</tbody>\n</table></figure></figure>","ord":2},{"label":"D","content_html":"<figure class=\"table left-justified\"><figure class=\"table left-justified\"><table border=\"1\">\n<tbody>\n<tr>\n<th style=\"text-align: center;  width: 57.3264px;\" scope=\"row\" id=\"90b2736e-9812-4861-8afa-f96f4b06820a_option_4_tableColumn_1\"><math alttext=\"x\"><mi>x</mi>\n</math></th>\n<td style=\"text-align: center;  width: 46.4931px;\" id=\"90b2736e-9812-4861-8afa-f96f4b06820a_option_4_tableColumn_2\"><math alttext=\"1\"><mn>1</mn>\n</math></td>\n<td style=\"text-align: center;  width: 33.4722px;\" id=\"90b2736e-9812-4861-8afa-f96f4b06820a_option_4_tableColumn_3\"><math alttext=\"2\"><mn>2</mn>\n</math></td>\n<td style=\"text-align: center;  width: 33.4722px;\" id=\"90b2736e-9812-4861-8afa-f96f4b06820a_option_4_tableColumn_4\"><math alttext=\"3\"><mn>3</mn>\n</math></td>\n</tr>\n<tr>\n<th style=\" text-align: center;\" scope=\"row\"><math alttext=\"h left parenthesis x right parenthesis\"><mi>h</mi><mfenced><mi>x</mi></mfenced></math></th>\n<td style=\" text-align: center;\"><math alttext=\"negative 2\"><mo>-</mo><mn>2</mn>\n</math></td>\n<td style=\" text-align: center;\"><math alttext=\"1\"><mn>1</mn>\n</math></td>\n<td style=\" text-align: center;\"><math alttext=\"3\"><mn>3</mn>\n</math></td>\n</tr>\n</tbody>\n</table></figure></figure>","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}}