|y| = f(x) is the f(x) graph without the part where f(x)<0 AND the reflection of this across the x axis
Yep it's true. It's a good idea to understand why this is true as well as just memorising it. The reason that it's true is that |y| >= 0 (so it cannot be <0) for any value of y, so you omit the section of the graph where f(x)<0 (i.e. omit the section below the x-axis). Also the reason for the reflection about the x axis is that |y| (the absolute value of the y-value you plot) must be equal to f(x), but the sign doesn't matter (can be negative or positive), so you have to plot both cases, so that's why it needs to be reflected.
|y| = |f(x)| is the f(x) graph AND the reflection of this across the x axis.
This is true too. The reason for this is that y=|f(x)| is equivalent graph of f(x) where f(x) >= 0 (above or on the x-axis), and the graph of -f(x) where f(x) is negative (below the x-axis). And to graph |y| = |f(x)|, use the principle above for |y| = f(x) where you cut off whatever is below the x-axis and then reflect it about the x-axis. But because |f(x)| >= 0 guaranteed, you won't need to cut off anything. That's why the graph of |y| = |f(x)| is just the graph of y=f(x) reflected about the x-axis, with NOTHING cut off.
