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Question 82150: If P(4,-5) is a point on the graph of the function y=f(x), find the corresponding point on the graph of y=2f(x-6). The answer is multiple choice.
a. (1,8)
b. (2,-5)
c. (6,8)
d. (10,-10)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! If we're given y=2f(x-6), this tells us is to shift the original graph f(x) 6 units to the right and double every output. So we're essentially starting at x=4 (the x-coordinate of our point), shifting 6 units to the right (adding 6 to 4), and then doubling the output. So our new x-coordinate is x=10. We can easily verify this by sticking x=10 into f(x-6) to get:
f(10-6)=f(4)
which is our original point. To get our new y coordinate, we simply double the output (ie our old y-coordinate y=-5). So the corresponding point on y=2f(x-6) is
(10,-10) which is answer d)
If this is hard to grasp, make a function that goes through (4,-5) (for instance  ) and shift the function. So y=2f(x-6) would be
y=2f(x-6)-> 
and if we plug in x=10 (remember we've shifted 6 units to the right) we get y=-10, which verifies our answer.
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