# SOLUTION: 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)

Algebra ->  -> SOLUTION: 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)       Log On

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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(29613)   (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.