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24 =-8 30 =-8 32 =8 Choice B is correct. According to the table, f^ h , f^ h , and f^ h . = + Let the quadratic function g be defined by g^xh f^xh 8. Therefore, 24 = 24 +8 30 = 30 +8 32 = 32 +8 - g^ h f^ h , g^ h f^ h , and g^ h f^ h . Substituting 8 for 24 24 = 24 +8 24 =-8+8 24 =0 f^ h in the equation g^ h f^ h yields g^ h , or g^ h . - 30 30 = 30 +8 30 =-8+8 Substituting 8 for f^ h in the equation g^ h f^ h yields g^ h , 30 =0 32 32 = 32 +8 or g^ h . Substituting 8 for f^ h in the equation g^ h f^ h yields 32 =8+8 32 =16 24 =0 30 =0 g^ h , or g^ h . By the factor theorem, if g^ h and g^ h , = -24 -30 32 =16 then g^xh k^x h^x h, where k is a constant. Since g^ h , 32 16 = -24 -30 substituting for x and for g^xh in the equation g^xh k^x h^x h 16= 32-24 32-30 16= 8 2 16=16 yields k^ h^ h, or k^ h^ h, which is equivalent to k. 16 = Dividing both sides of this equation by yields 1 k. Substituting 1 for k in the = -24 -30 = -24 -30 equation g^xh k^x h^x h yields g^xh ^x h^x h. Since = + - = g^xh f^xh 8, it follows that g^xh 8 f^xh. Subtracting 8 from both sides of the = -24 -30 -8= -24 -30 -8 equation g^xh ^x h^x h yields g^xh ^x h^x h . Substituting - = -24 -30 -8 f^xh for g^xh 8 in this equation yields f^xh ^x h^x h . 47 SAT PRACTICE TEST #11 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2 =24 Choice A is incorrect. If this equation defined f, then when x , the value of - f^xh would be 4, not 8. Choice C is incorrect. If this equation defined f, then =32 32 when x , the value of f^xh would be , not 8. Choice D is incorrect. If this =32 -32 equation defined f, then when x , the value of f^xh would be , not 8.