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x f(x) 0 2 9 1 3 2 2 3 5 For the linear function f, the table shows three values f(x) of x and their corresponding values of. Which f(x) equation defines? f(x)
Correct answer: A (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice A is correct. An equation that defines a linear function f can be written ( ) = + in the form f x mx b, where m and b are constants. It’s given in the table = ( )= ( ) that when x 0, f x 29. Substituting 0 for x and 29 for f x in the equation ( ) = + (=) + = f x mx b yields 29 0 m , or b29 b. Substituting 29 for b in the ( ) = + ( ) = + equation f x mx b yields f x mx 29. It’s also given in the table that = ( )= ( ) when x 1, f x 32. Substituting 1 for x and 32 for f x in the equation 35 SAT PRACTICE TEST #4 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS nnn MATH: MODULE 1 ( ) = + (=) + = + f x mx 29 yields 32 m 1 29, or 32 m 29. Subtracting 29 from = both sides of this equation yields 3 m. Substituting 3 for m in the equation ( ) = + ( ) = + f x mx 29 yields f x 3 x 29. Choice B 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 and may result from conceptual or calculation errors.
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