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Math Help - Domain/Range and Absolute values

  1. #1
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    Domain/Range and Absolute values

    1.) state the domain and range of each relation, then determine if the relation is a function.

    a) y= -2(x+1)^2-3

    b) y=1/x+3

    c) 2sinx


    2.) Evaluate

    a) l-22l / l-11l + -16/ l-4l
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  2. #2
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    Quote Originally Posted by Skoz View Post
    1.) state the domain and range of each relation, then determine if the relation is a function.

    a) y= -2(x+1)^2-3
    The domain are all real x.
    Remember that (x+1)^2\geq 0 \implies -2(x+1)^2 \leq 0 \implies -2(x+1)^2 \leq -3 so the range is y\leq -3.

    b) y=1/x+3
    The domain are all x\not = 0.
    As for the range we have y>3 \text{ or }y<-3.
    To see this picture the hyperbola y=x and shift it up 3 units.

    c) 2sinx
    The domain are all real x and remember that -1\leq \sin x\leq 1 \implies -2\leq 2\sin x\leq 2.
    Thus, range is |y|\leq 2.
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