f(x) = (x+6)(x+5)(x−4) The function fis given. Which table of values = f(x)−3 represents y?
Correct answer: B (parsed from the explanation — this source omits an answer key for this item)
Explanation
= +6 +5 -4 = - Choice B is correct. It’s given that f^xh ^x h^x h^x h and y f^xh 3. +6 +5 -4 = - Substituting ^x h^x h^x h for f^xh in the equation y f^xh 3 yields = +6 +5 -4-3 - y ^x h^x^ hhx . Substituting 6 for x in this equation yields = -6+6 -6+5 -6-4-3 =- - y ^ h^ h^h , or y 3. Substituting 5 for x in the = +6 +5 -4-3 = -5+6 -5+5 -5-4-3 equation y ^x h^x^ hhx yields y ^ h^ h^h , or =- = +6 +5 -4-3 y 3. Substituting 4 for x in the equation y ^x h^x^ hhx yields = 4+6 4+5 4-4-3 =- =- =- y ^ h^ h^h , or y 3. Therefore, when x 6 then y 3, =- =- = =- when x 5 then y 3, and when x 4 then y 3. Thus, the table of values = - in choice B represents y f^xh 3. 35 SAT PRACTICE TEST #9 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1 = - = - Choice A is incorrect. This table represents y x3 rather than y f^xh 3. = + = - Choice C is incorrect. This table represents y x3 rather than y f^xh 3. = + = - Choice D is incorrect. This table represents y f^xh 3 rather than y f^xh 3.
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