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Thread: absolute value graphs

  1. #1
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    absolute value graphs

    How do you graph lyl-lxl=2?
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  2. #2
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    Hello, lilmolldoll41!

    I had to baby-talk my way through this one.
    . . I hope it makes sense . . .


    How do you graph: .$\displaystyle |y| - |x| \:=\:2$ ?

    We have: .$\displaystyle |y| \:=\:|x| + 2$


    First, we consider: .$\displaystyle y \:=\:|x| + 2$

    The graph of $\displaystyle y \:= \:|x|$ is a V-shape with its vertex at the origin.

    The graph of $\displaystyle y \:=\:|x| + 2$ is the same graph moved up 2 units.
    Code:
                      |
              \       |       /
                \     |     /
                  \   |   /
                    \ | /
                      *
                      |
          ------------+------------
                      |

    Now $\displaystyle |y|$ makes the graph symmetric to the x-axis.
    . . (Whatever happens above the x-axis also happens below.)

    So the "V" is reflected downward and the graph looks like this:
    Code:
                      |
              \       |       /
                \     |     /
                  \   |   /
                    \ | /
                      *
                      |
          ------------+------------
                      |
                      *
                    / | \
                  /   |   \
                /     |     \
              /       |       \
                      |
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