The function f ( x ) is defined as 19 more than 4 times a number x . If y

Question

The function f ( x ) is defined as 19 more than 4 times a number x . If y = f ( x ) is graphed in the x y -plane, what is the best interpretation of the x -intercept?

Accepted Answer

Choice A is correct. It&rsquo;s given that the function f ( x ) is defined as 19 more than 4 times a number x . This can be represented by the equation f ( x ) = 4 x + 19 . The x -intercept of the graph of y = f ( x ) in the xy -plane is the point where the graph intersects the x -axis, or the point on the graph where the value of f ( x ) is equal to 0 . Substituting 0 for f ( x ) in the equation f ( x ) = 4 x + 19 yields 0 = 4 x + 19 . Subtracting 19 from each side of this equation yields - 19 = 4 x . Dividing each side of this equation by 4 yields x = - 19 4 . Therefore, when f ( x ) = 0 , the number is - 19 4 . Choice B is incorrect. This is the best interpretation of the y -intercept, not the x -intercept, of the graph of the function. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect. This is the best interpretation of the slope, not the x -intercept, of the graph of the function.

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