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Question 1187670: Suppose (5,−5) is a point on the graph of y=f(x). What is a point that will be on the graph of y=−6f(x)+6?
I'm very confused on how to solve this... I can't seem to graph the y=-6f(x)+6 part because of the two variables and I'm not sure what steps to take, could someone please explain what I have to do and step me through the process?
Answer by ikleyn(52832)   (Show Source):
You can put this solution on YOUR website! .
Suppose (5,−5) is a point on the graph of y=f(x).
What is a point that will be on the graph of y=−6f(x)+6?
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The plot of y = -6f(x) + 6 is obtained from the parent plot y = f(x) by stretching y-axis 6 times, then reflecting about x-axis
and then shifting 6 units up.
THEREFORE, since the point (5,-5) was originally on the parent plot y = f(x),
we FIRST move this point to the new position (5,-30),
THEN reflect this point (5,-30) about x-axis, getting the point (5,30),
and AFTER THAT we move this point (5,30) six units up, getting finally the point (5,36).
This procedure does not depend on what the function f(x) is concretely: it works for ANY function f(x).
At this point, I completed my explanation. Do you understand everything in FULL ?
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When you work/solve such problems, you should firmly know that the first coordinate in pair (x,y) is x-coordinate,
while the second number in this pair is y-coordinate.
You should know it f i r m l y and operate with it F R E E L Y ( ! )
It is very important ( ! )
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