Help graphing f(|x|)

A student asked me today about what happens to y = f(x) when you do y = f(|x|). To me, it seemed like every negative x you plugged in there would become positive because of absolute value, so only the right hand side of the graph would get graphed.

I know that y = |f(x)| makes all the y's positive, so any part that's in the negative region gets flipped up to the positive side, but I'm confused about y = f(|x|). Thanks.

y = |f(x)| will reflect across the x-axis those pieces of f(x) which are negative. All of f(x) will still get graphed, just none of it will be negative.

y = f(|x|) on the other hand, will only graph what is on the positive-x side. What will appear on the negative-x side will be a reflection of what is on the positive-x side. The biggest differences is that y = f(|x|) doesn't pick up all the values of f(x), it only picks up what is on the right of the y-axis and simply reflects that onto the left side. This also means that y = f(|x|) can attain negative values, whereas y = |f(x)| cannot.


They both do essentially the same thing, reflect pieces of the graph over either the x-axis or the y-axis, but the outcomes are VASTLY different.


YES, a concrete example. Thanks. I'll do my best to draw 11. and 12. in this text box to give you a rough idea of the shapes. Ignore the periods, they're for spacing purposes.
y = f(x):
............/.|\.............
........./....|.\.............
....../.......|..\............
.../..........|...\...........
/.............|....\..........
--------------------\---------
..............|......\....../.
..............|.......\..../..
..............|........\../...
..............|.........\/....
..............|...............


y = |f(x)|
............/.|\......../\...
........./....|.\....../..\...
....../.......|..\..../....\..
.../..........|...\../......\.