If I have a picture of a graph f(x), how can I draw what |f(x)| and 3f(x-2) look like?

This is about a topic called graph transformations. It can get quite complicated, but the lucky thing here is that each question can be broken down into steps.

So considering the first question with |f(x)|, the | | signs mean that you have to make your answer positive at the end. So if f(5) was -2, |f(5)| = 2. This means that whenever the graph "dips below" the x-axis, we have to reflect it back up, so we can see the positive version. So to draw |f(x)| is quite simple.

For 3f(x-2), we have to first see what 3f(x) looks like, then what f(x-2) looks like. So for 3f(x), you simply need to multiply each output (y-coordinate) by 3. The x-coordinates can't be affected, because f(x) is left on its own. So if f(2) =6, then 3f(2) = 18. It "stretches the graph!". The important things they'll be looking for in the exam are for a few specific points so make sure you multiply only the y coordinate by 3 to ensure they know you know what you're talking about.

Now for f(x-2), this is a "shift" on the x-axis. It has no effect on the y-axis, as everything is going on "inside" the function. As it's x-2, what was previously happening when x=2 now happens at x=4 for example, and what happened at 0 now happens at 2. Can you see that the graph would have to move right by 2? Remember, this can only affect the x-coordinates. All that's left to do now is combine them together, so shift the graph to the right by 2, so all the x coordinates have two added to them, and times each y-coordinate by 3.