f x = a - 19 x + 5 In the given function f , a is a constant. The

Question

f x = a - 19 x + 5 In the given function f , a is a constant. The graph of function f in the xy -plane, where y = f x , is translated 3 units down and 4 units to the right to produce the graph of y = g x . Which equation defines function g ?

Accepted Answer

Choice B is correct. It's given that the graph of y = g x is produced by translating the graph of y = f x 3 units down and 4 units to the right in the xy -plane. Therefore, function g can be defined by an equation in the form g x = f x - 4 - 3 . Function f is defined by the equation f x = a - 19 x + 5 , where a is a constant. Substituting x - 4 for x in the equation f x = a - 19 x + 5 yields f x - 4 = a - 19 x - 4 + 5 . Substituting a - 19 x - 4 + 5 for f x - 4 in the equation g x = f x - 4 - 3 yields g x = a - 19 x - 4 + 5 - 3 , or g x = a - 19 x - 4 + 2 . Therefore, the equation that defines function g is g x = a - 19 x - 4 + 2 . Choice A is incorrect. This equation defines a function whose graph is produced by translating the graph of y = f x 3 units down and 4 units to the left, not 3 units down and 4 units to the right. Choice C is incorrect. This equation defines a function whose graph is produced by translating the graph of y = f x 4 units to the left, not 3 units down and 4 units to the right. Choice D is incorrect. This equation defines a function whose graph is produced by translating the graph of y = f x 4 units to the right, not 3 units down and 4 units to the right.

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