The function f is defined by f x = x - 6 x - 2 x + 6 . In

Question

The function f is defined by f x = x - 6 x - 2 x + 6 . In the xy -plane, the graph of y = g x is the result of translating the graph of y = f x up 4 units. What is the value of g 0 ?

Accepted Answer

The correct answer is 76 . It's given that the graph of y = g x is the result of translating the graph of y = f x up 4 units in the xy -plane. It follows that the graph of y = g x is the same as the graph of y = f x + 4 . Substituting g x for y in the equation y = f x + 4 yields g x = f x + 4 . It's given that f x = x - 6 x - 2 x + 6 . Substituting x - 6 x - 2 x + 6 for f x in the equation g x = f x + 4 yields g x = x - 6 x - 2 x + 6 + 4 . Substituting 0 for x in this equation yields g 0 = 0 - 6 0 - 2 0 + 6 + 4 , or g 0 = 76 . Thus, the value of g 0 is 76 .

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