Question

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 y-axis. Third, shift the graph 2 units to the right. Fourth, stretch the graph vertically by 2. Lastly, shift the graph 4 units downward.

Answer 1

" 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(x-2). 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.