Thread: Absolute Value Graphs

Hi

For y = abs(x+2) + abs(x) + abs(x-2), what are the cases?

I know if there were only two abs, there would be three cases to work out but I have no clue how many there will be for this question and what they might be.

Thanx

Dear xwrathbringerx,

the abs(x) function behaves "irregular" at x=0 that is x=0 is a singular point.
Therefore the function abs(x-2) has sigularity at x=2, hasn't it?

So in your problem you have to divide into 4 cases because there are 3 singular point.

If then .
If then .
If then .
If then .

The graph is attached.

Hello, xwrathbringerx!

Another approach . . .

For , what are the cases?

Make a sketch . . .

The graph of . .is a with its vertex at the origin.

The graph of . .is the same graph moved 2 units to the right.

The graph of . .is the same graph moved 2 units to the left.

Code:

      \    \    |    /    /
       \    \   |   /    /
        \    \  |  /    /
         \    \ | /    /
          \    \|/    /
      \    \    *    /    /
       \    \  /|\  /    /
        \    \/ | \/    /
         \   /\ | /\   /
          \ /  \|/  \ /
  ---------*----*----*-------
          -2    |    2

Then add the ordinates.

We get the graph that james_bond so thoughtfully provided.