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t__ The function f is defined by f(x) = a x+b, where a and b are constants. In the xy-plane, the graph of = f(x) (−24,0) y passes through the point, and f(24) < 0. Which of the following must be true? f(0) = 24
Correct answer: D (parsed from the explanation — this source omits an answer key for this item)
Explanation
24 10 24 Choice D is correct. It’s given that f^ h . Substituting for f^xh in the = + 24 = 24+ 24+ 10 equation f^xh a x b yields f^ h a b. Therefore, a b . Since 24+ 1 b can’t be negative, it follows that a 0. It’s also given that the graph of = -24,0 =-24 = y f^xh passes through the point ^ h. It follows that when x , f^xh 0. -24 = + Substituting for x and 0 for f^xh in the equation f^xh a x b yields 0= -24+ = -24+ =0 a b. By the zero product property, either a 0 or b . 1 24+ =0 Since a 0, it follows that b . Squaring both sides of this equation yields -24+ =0 24 =24 b . Adding to both sides of this equation yields b . Since 1 24 1 a 0 and b is , it follows that a b must be true. Choice A is incorrect. The value of f^0h is a b, which must be negative. Choice B -24 is incorrect. The value of f^0h is a b, which could be , but doesn’t have to be. Choice C is incorrect and may result from conceptual or calculation errors. 50 SAT PRACTICE TEST #6 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2
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