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.

" 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.

To find the graph of 2f(-3x - 2) - 4, you need to follow the steps correctly.

First, compressing the graph horizontally by a factor of 3 means you need to replace x with -x/3. This results in 2f(-x - (2/3)) - 4.

Next, reflecting the graph over the y-axis means you need to replace f(-x - (2/3)) with f(x + (2/3)). The equation becomes 2f(x + (2/3)) - 4.

Then, shifting the graph 2 units to the right means you need to subtract 2 from the equation. It becomes 2f(x + (2/3)) - 6.

After that, stretching the graph vertically by a factor of 2 means you need to multiply the equation by 2. It becomes 4f(x + (2/3)) - 6.

Lastly, shifting the graph 4 units downward means you need to subtract 4 from the equation. It becomes 4f(x + (2/3)) - 10.

Therefore, the correct equation for the graph is 4f(x + (2/3)) - 10.