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?
~~~~~~~~~~~~~~~~~~~



<pre>
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).
</pre>

At this point, &nbsp;I &nbsp;completed my explanation.  &nbsp;&nbsp;Do you understand everything in &nbsp;FULL ?



////////////



When you work/solve such problems, &nbsp;you should firmly know that the first coordinate in pair &nbsp;(x,y) &nbsp;is &nbsp;x-coordinate, 

while the second number in this pair is &nbsp;y-coordinate.



You should know it &nbsp;&nbsp;<U>f i r m l y</U> &nbsp;&nbsp;and operate with it &nbsp;&nbsp;<U>F R E E L Y</U> &nbsp;(&nbsp;!&nbsp;)



It is very important &nbsp;(&nbsp;!&nbsp;)