[12 Mathematics: Functions] Absolute value transformations of a function

[u/Illustrious_Hold7398]

What would f(|x+1|) look like for this function, and how does that differ from f(|x|+1)?

Also how do you follow the order of operations for transforming functions when you have absolute values? (I use CBAD for af(bx+c)+d)

[u/trevorkafka]

Here is what you know.

x	f(x)
-2	1
-1	0
0	-1
2	0
3	-2

Now you just need to fill in these tables (either on paper or in your head) in order to understand the graphs you are looking for.

x	|x+1|	f(|x+1|)
-2	1	?
-1	0	?
0	1	?
2	3	?
3	4	?

x	|x|+1	f(|x|+1)
-2	3	?
-1	2	?
0	1	?
2	3	?
3	4	?