In the linear function f , f 0 = 8 and f 1 = 12 . Which equation defines f

Question

In the linear function f , f 0 = 8 and f 1 = 12 . Which equation defines f ?

Accepted Answer

Choice D is correct. Since f is a linear function, it can be defined by an equation of the form f x = a x + b , where a and b are constants. It's given that f 0 = 8 . Substituting 0 for x and 8 for f x in the equation f x = a x + b yields 8 = a 0 + b , or 8 = b . Substituting 8 for b in the equation f x = a x + b yields f x = a x + 8 . It's given that f 1 = 12 . Substituting 1 for x and 12 for f x in the equation f x = a x + 8 yields 12 = a 1 + 8 , or 12 = a + 8 . Subtracting 8 from both sides of this equation yields a = 4 . Substituting 4 for a in the equation f x = a x + 8 yields f x = 4 x + 8 . Therefore, an equation that defines f is f x = 4 x + 8 . Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors.

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