SOLUTION: How did they change the graph of y = f(x) by making it: (a) y = 2f(x + 8) - 7 (b) y = 2f(x - 8) + 7

First

1. They replaced x by x+8, which shifted the graph 8 units LEFT.  That gave:

y = f(x + 8)

then

2. They multiplied the right side by a factor of 2, which STRETCHED the graph
   vertically by a factor of 2.  That gave:

y = 2f(x + 8)

then

3. They subtracted 7 from the right side, which SHIFTED the graph DOWN by 
   7 units. That gave

y = 2f(x + 8) - 7

So the correct choice was the middle one:

Shift left 8 units, stretch vertically by a factor of 2, then shift down 
7 units.

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First

1. They replaced x by x-8, which shifted the graph 8 units RIGHT.
   That gave:

y = f(x - 8)

   then

2. They multiplied the right side by a factor of 2, which STRETCHED 
   the graph vertically by a factor of 2.  That gave:

y = 2f(x - 8)

then

3. They added 7 to the right side, which SHIFTED the graph UP by 
   7 units. That gave

y = 2f(x - 8) + 7

So the correct choice was the middle one:

Shift right 8 units, stretch vertically by a factor of 2, then shift up
7 units.

---------------------------

Edwin