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Thread: Domain and Range of h(x)=5−2(x)?

  1. #1
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    Domain and Range of h(x)=5−2(x)?

    How do I find the Domain and Range of the function

    h(x)=5−2(x)

    Thank you!
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  2. #2
    MHF Contributor alexmahone's Avatar
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    $\displaystyle h(x)=5-2^x$

    The domain of h(x) is $\displaystyle R$.

    --------------------------------------

    $\displaystyle 2^x>0$

    $\displaystyle -2^x<0$

    $\displaystyle 5-2^x<5$

    The range for $\displaystyle h(x) = 5 - 2^x$ is $\displaystyle (-\infty, 5).$
    Last edited by alexmahone; Jul 16th 2009 at 04:08 AM.
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  3. #3
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    Quote Originally Posted by Polyxendi View Post
    How do I find the Domain and Range of the function

    h(x)=5−2ˆ(x)

    Thank you!
    The domain of $\displaystyle h(x) = 5 - 2^x$ is all real numbers.

    For the range, apply the transformations one-by-one:
    The range for $\displaystyle y = 2^x$ (the parent function) is (0, ∞).
    The range for $\displaystyle y = -2^x$ (reflection across the x-axis) would be (-∞, 0).
    The range for $\displaystyle h(x) = 5 - 2^x$ is (-∞, 5).


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