calculus reposted
posted by Blake .
Given the graph of f(x) find the graph of 2 f( 3x  2)  4
Is this correct???
First, compress the graph horizontally by 3. Second, reflect the graph over the yaxis. Third, shift the graph 2 units to the right. Fourth, stretch the graph vertically by 2. Lastly, shift the graph 4 units downward.

" Third, shift the graph 2 units to the right."
This step is wrong. What this would do is transform a function g(x) to g(x2). But what you have after perforing the forst to steps is the function f(3x) which you want to transform into
f(3x 2). Clearly, you have to change x according to:
x > x + 2/3
to get the desired transform for f(3x)
So, the graph of g(x) = f(3x) shifts by 2/3 to the left.