The function f is defined by f ( x ) = ( - 8 ) ( 2 ) x +

Question

The function f is defined by f ( x ) = ( - 8 ) ( 2 ) x + 22 . What is the y -intercept of the graph of y = f ( x ) in the xy -plane?

Accepted Answer

Choice A is correct. The y -intercept of the graph of y = f x in the xy -plane occurs at the point on the graph where x = 0 . In other words, when x = 0 , the corresponding value of f x is the y -coordinate of the y -intercept. Substituting 0 for x in the given equation yields f 0 = - 8 2 0 + 22 , which is equivalent to f 0 = - 8 1 + 22 , or f 0 = 14 . Thus, when x = 0 , the corresponding value of f x is 14 . Therefore, the y -intercept of the graph of y = f x in the xy -plane is 0 , 14 . 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. This could be the y -intercept for f x = - 8 2 x , not f x = - 8 2 x + 22 .

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