{"id":"cb_question_bank:23f75900-dc08-4156-b21b-a505d2cca7f9","source_id":"cb_question_bank","source_item_id":"23f75900-dc08-4156-b21b-a505d2cca7f9","external_id":null,"ibn":"029595-DC","question_id":"9654add7","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"f of x equals, negative 500, x squared, plus 25,000 x The revenue f of x , in dollars, that a company receives from sales of a product is given by the function f above, where x is the unit price, in dollars, of the product. The graph of y equals f of x in the xy -plane intersects the x -axis at 0 and a . What does a represent?","stimulus":"","stimulus_html":null,"stem_html":"

\n \n \"f\n

The revenue \"f, in dollars, that a company receives from sales of a product is given by the function f above, where x is the unit price, in dollars, of the product. The graph of \"y in the xy-plane intersects the x-axis at 0 and a. What does a represent?

\n","rationale_html":"

Choice C is correct. By definition, the y-value when a function intersects the x-axis is 0. It’s given that the graph of the function intersects the x-axis at 0 and a, that x is the unit price, in dollars, of a product, and that \"f, where \"y, is the revenue, in dollars, that a company receives from the sales of the product. Since the value of a occurs when \"y, a is the unit price, in dollars, of the product that will result in a revenue of $0.

Choice A is incorrect. The revenue, in dollars, when the unit price of the product is $0 is represented by \"f, when \"x. Choice B is incorrect. The unit price, in dollars, of the product that will result in maximum revenue is represented by the x-coordinate of the maximum of f. Choice D is incorrect. The maximum revenue, in dollars, that the company can make is represented by the y-coordinate of the maximum of f.

\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.626000+00:00","source_updated_at":"2023-08-02T20:25:59.626000+00:00","options":[{"label":"A","content_html":"

The revenue, in dollars, when the unit price of the product is $0

\n","ord":0},{"label":"B","content_html":"

The unit price, in dollars, of the product that will result in maximum revenue

\n","ord":1},{"label":"C","content_html":"

The unit price, in dollars, of the product that will result in a revenue of $0

\n","ord":2},{"label":"D","content_html":"

The maximum revenue, in dollars, that the company can make

\n","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}}