I am attempting to study college algebra 
on my own. There are some questions that 
do not make sense to me. I want to take 
my college algebra sometime this spring. 
please help me get up to par.  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) I thank you in 
advance for any assistance in this matter.

Y = f(x)

Two things have been done to f(x)

1. First x has been replaced by x-6 to give

y = f(x-6)

This shifted the graph 6 units to the RIGHT.
So, in particular, the point (4,-5) has been 
shifted right to the point (10,-5)

2. Then the expression f(x) has been 
multiplied by 2 to give

y = 2f(x-6)

This STRETCHED the graph by a factor of 2 
making the point 2 times as far from the 
x-axis as it was before it was multiplied 
by 2. So, in particular, the point (10,-5) 
has been stretched to the point (10,-10).

Edwin