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Math Help - domain and range of a absolute value function

  1. #1
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    Lightbulb domain and range of a absolute value function

    Hey

    Having some trouble with this one.

    Find the domain and range of f(x) = -2|-2+x|

    Thanks
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  2. #2
    Senior Member
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    Smile

    Quote Originally Posted by smplease View Post
    Hey

    Having some trouble with this one.

    Find the domain and range of f(x) = -2|-2+x|

    Thanks
    the domain is all x \in \mathbb{R}

    to find the range,. consider the case when -2+x \geq 0 and -2+x < 0

    good luck
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  3. #3
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    Hello, smplease!

    Did you make a sketch?


    Find the domain and range of: . f(x) = -2|-2+x|

    We have: . f(x) \:=\:-2|x-2|


    You should know the graph of: . f(x) \:=\:|x|
    . . It is a \vee with its vertex at the origin.

    The graph of: . f(x) \:=\:|x-2| .is the previous graph moved 2 units to the right.

    The graph of: . f(x) \:=\:-2|x-2| .is the previous graph
    . . reflected over the x-axis and is "steeper".


    Hence, the graph of f(x) \:=\:-2|x-2| looks like this:
    Code:
                |
                |   2
          - - - + - * - - - -
                |  / \
                | /   \
                |/     \
                /       \
               /|        \
                |


    Got it?

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