Question 354336
suppose that f and g are functions. Suppose further that we can write g in terms of f as follows: 
g(x)=f(x-3)+5 
List a sequence of transformations that will transform the graph of f into a graph of g. 
I am at a loss of how to even break this down into a description with words. Can anyone explain this to me? Thank you, thank you in advance.

<pre>
We begin by starting with f(x) and building up the new expressing by
following this order of operations.  I am giving you all of them but
for this problem you only need to use steps 5 and 6:

1. Replace x by -x to reflect the graph horizontally across the y-axis.

2. Replace x by ax, a > 0 to shrink the graph horizontally if a > 1 or stretch
the graph horizontally if positive number a < 1, by a factor of a.

3. Multiply the entire expression by positive number b to shrink the graph
vertically if b < 1, or stretch the graph vertically if b > 1, by a factor of
b.  

4. Multiply the entire expression by -1 to reflect the graph across the x-axis.

5. Replace x by (x-c), c > 0, to shift the graph right c units, or by (x+c)
to shift the graph left c units.

6. Add d, d > 0, to the right side of the entire expression to shift the graph
upward by d units, or subtract d from the right side to shift the graph
downward by d units.

      
As I said above, you only need steps 5 and 6, to go from 

f(x) 

to 

f(x-3)+5

We start with 

f(x)

We use (5)

We replace x by (x-3), 3 > 0, to shift the graph right 3 units

We get:

f(x-3)

We use (6)

We add 5, d > 0, to the right side of the entire expression to shift the graph
upward by 5 units.

We get

f(x-3)+5

So the transformations are 

Shift the graph right 3 units, then shift the graph upward 5 units.

Edwin</pre>