Question 43501
<pre><font size = 5><b>
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)
 
{{{ graph(400, 400, -20, 20, -20, 20, -5+sqrt(.2-(x-4)^2), -5-sqrt(.2-(x-4)^2) )  }}}

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

y = f(x-6)

{{{ graph(400, 400, -20, 20, -20, 20, -5+sqrt(.2-(x-10)^2), -5-sqrt(.2-(x-10)^2) )  }}} 

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)

{{{ graph(400, 800, -20, 20, -40, 40, 2(-5+sqrt(.2-(x-10)^2)), 2(-5-sqrt(.2-(x-10)^2)) )  }}}

Edwin
AnlytcPhil@aol.com</pre>