If the graph of y = f(x) is transformed into the graph of 2y - 6 = - 4 f(x - 3), point (a , b) on the graph of y = f(x) becomes point (A , B) on the graph of 2y - 6 = - 4 f(x - 3) where A and B are given by Choose the correct choice from the following answers
A) A = a - 3, B = b	B) A = a - 3, B = b2	C) A = a + 3, B = -2 b	D) A = a + 3, B = -2 b +3	E) None
Solution   We first solve 2y - 6 = - 4 f(x - 3) for y.   y = - 2 f(x - 3) + 3   The graph of y = - 2 f(x - 3) + 3 is that of y = f(x) shifted 3 units to the right, stretched vertically by a factor of 2, reflected on the x axis and shifted up by 3 units. A point of y = f(x) will undergo the same transforamtions. Hence   Point (a , b) on the graph of y = f(x)   Becomes (a + 3 , b) on the graph of y = f(x - 3) : shifted 3 units to the right   Becomes ( a + 3 , 2 b) on the graph of y = 2 f(x - 3) : stretched vertically by 2   Becomes ( a + 3 , - 2 b) on the graph of y = - 2 f(x - 3): reflected on x axis   Becomes ( a + 3 , - 2 b + 3) on the graph of y = - 2 f(x - 3) + 3 : shifted up 3 units   Answer A = a + 3, B = -2 b +3
<result>D</result>
If the graph of y = f(x) is transformed into the graph of 2y - 6 = - 4 f(x - 3), point (a , b) on the graph of y = f(x) becomes point (A , B) on the graph of 2y - 6 = - 4 f(x - 3) where A and B are given by