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). Not sure but I 
think it is (6,8).  Thanks for looking it over. 

I'm afraid that's wrong.

y = 2f(x-6)

This requires two operations of y = f(x)

1. First we go from

y = f(x)

to

y = f(x-6)

That shifts the graph 6 units right.
So the point (4,-5)
 


moves right to the point (10, -5) on the graph of

y = f(x-6)

 

2. Then we go from

y = f(x-6)

to

y = 2f(x-6) 

That stretches the graph double vertically.
Imagine the graph drawn on a rubber sheet
and stretched double vertically.  The points
above the x-axis will stretch twice as high
and the points below the x-axis will stretch
twice as low.  Therefore the point (10. -5), 
being below the x-axis, will stretch twice
as low or down to (10, -10)



Edwin
AnlytcPhil@aol.com