The functions f and g are defined as f ( x ) = 1 4 x - 9 and g

Question

The functions f and g are defined as f ( x ) = 1 4 x - 9 and g ( x ) = 3 4 x + 21 . If the function h is defined as h ( x ) = f ( x ) + g ( x ) , what is the x -coordinate of the x -intercept of the graph of y = h x in the xy -plane?

Accepted Answer

The correct answer is - 12 . It's given that the functions f and g are defined as f x = 1 4 x - 9 and g x = 3 4 x + 21 . If the function h is defined as h x = f x + g x , then substituting 1 4 x - 9 for f x and 3 4 x + 21 for g x in this function yields h x = 1 4 x - 9 + 3 4 x + 21 . This can be rewritten as h x = 4 4 x + 12 , or h x = x + 12 . The x -intercept of a graph in the xy -plane is the point on the graph where y = 0 . The equation representing the graph of y = h x is y = x + 12 . Substituting 0 for y in this equation yields 0 = x + 12 . Subtracting 12 from both sides of this equation yields - 12 = x , or x = - 12 . Therefore, the x -coordinate of the x -intercept of the graph of y = h x in the xy -plane is - 12 .

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