{"id":"cb_question_bank:ef4c9cd0-eb20-40dc-915d-9b2e4fe459cf","source_id":"cb_question_bank","source_item_id":"ef4c9cd0-eb20-40dc-915d-9b2e4fe459cf","external_id":"5af7e994-3850-4c5c-987d-1213c4f6baf8","ibn":null,"question_id":"4d037075","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Moving from left to right: The curve is in quadrant 3. The curve trends down sharply. As x increases, the curve approaches the line x equals negative 4. As x decreases, the curve approaches the line y equals 0. The curve passes through the following points: (negative 7 comma negative 2) (negative 6 comma negative 3) (negative 5 comma negative 6) The rational function f is defined by an equation in the form f left parenthesis x right parenthesis equals StartFraction a Over x plus b EndFraction , where a and b are constants. The partial graph of y equals f left parenthesis x right parenthesis is shown. If g left parenthesis x right parenthesis equals f left parenthesis x plus 4 right parenthesis , which equation could define function g ?","stimulus":"","stimulus_html":null,"stem_html":"

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

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The rational function f\n is defined by an equation in the form fx=ax+b, where a\n and b\n are constants. The partial graph of y=fx is shown. If  gx=fx+4, which equation could define function g\n?

","rationale_html":"

Choice C is correct. It's given that fx=ax+b and that the graph shown is a partial graph of y=fx. Substituting y\n for fx in the equation fx=ax+b yields \n\ty\n\t=\n\t\n\t\t\ta\n\t\t\t\n\t\t\t\tx\n\t\t\t\t+\n\t\t\t\tb\n\t\t\t\n\t\t\n\n. The graph passes through the point -7,-2. Substituting -7\n for x\n and -2\n for y\n in the equation \n\ty\n\t=\n\t\n\t\t\ta\n\t\t\t\n\t\t\t\tx\n\t\t\t\t+\n\t\t\t\tb\n\t\t\t\n\t\t\n\n yields -2=a-7+b. Multiplying each side of this equation by -7+b yields -2-7+b=a, or 14-2b=a. The graph also passes through the point -5,-6. Substituting -5\n for x\n and -6\n for y\n in the equation \n\ty\n\t=\n\t\n\t\t\ta\n\t\t\t\n\t\t\t\tx\n\t\t\t\t+\n\t\t\t\tb\n\t\t\t\n\t\t\n\n yields -6=a-5+b. Multiplying each side of this equation by -5+b yields -6-5+b=a, or 30-6b=a. Substituting 14-2b for a\n in this equation yields 30-6b=14-2b. Adding \n\t6\n\tb\n\n to each side of this equation yields 30=14+4b. Subtracting 14\n from each side of this equation yields \n\t16\n\t=\n\t\n\t\t4\n\t\tb\n\t\n\n. Dividing each side of this equation by 4\n yields \n\t4\n\t=\n\tb\n\n. Substituting 4\n for b\n in the equation 14-2b=a yields 14-24=a, or \n\t6\n\t=\n\ta\n\n. Substituting 6\n for a\n and 4\n for b\n in the equation fx=ax+b yields fx=6x+4. It's given that gx=fx+4. Substituting \n\tx\n\t+\n\t4\n\n for x\n in the equation fx=6x+4 yields fx+4=6x+4+4, which is equivalent to fx+4=6x+8. It follows that gx=6x+8.

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Choice A is incorrect. This could define function g\n if gx=fx-4.

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Choice B is incorrect. This could define function g\n if gx=fx.

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Choice D is incorrect. This could define function g\n if gx=fx·x+4.

","correct_answer":["C"],"has_media":true,"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":[{"label":"A","content_html":"

gx=6x

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

gx=6x+4

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

gx=6x+8

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

gx=6(x+4)x+4

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