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x f(x) –4 0 19 – 1 5 18 – 2 5 For the linear function f, the table shows three values of x and their corresponding values of f ( x). If h(x) = f(x)−13, which equation defines h? = 5x−4
Correct answer: B (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice B is correct. An equation that defines a linear function f can be written in = + the form f^xh mx b, where m and b are constants. It’s given in the table that =- = - when x 4, f^xh 0. Substituting 4 for x and 0 for f^xh in the equation = + 0= -4 + 0=-4 + f^xh mx b yields m^ h b, or m b. Adding 4m to both sides of = = + this equation yields 4m b. Substituting 4m for b in the equation f^xh mx b 19 = + =- = yields f^xh mx 4m. It’s also given in the table that when x 5, f^xh 1. 19 - = + Substituting 5 for x and 1 for f^xh in the equation f^xh mx 4m yields 1= - 19 +4 1= 1 mb 5 l m, or 5m. Multiplying both sides of this equation by 5 yields = = + =5 +4 5 m 5. Substituting 5 for m in the equation f^xh mx 4m yields f^xh x ^ h, =5 +20 = -13 5 +20 or f^xh x . If h^xh f^xh , substituting x for f^xh in this equation = 5 +20 -13 =5 +7 yields h^xh ^ x h , or h^xh x . Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect. This is an equation that defines the linear function f, not h. 44 SAT PRACTICE TEST #7 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2
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