How do I find the Domain and Range of the function

h(x)=5−2ˆ(x)

Thank you!

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- Jul 16th 2009, 03:00 AMPolyxendiDomain and Range of h(x)=5−2ˆ(x)?
How do I find the Domain and Range of the function

h(x)=5−2ˆ(x)

Thank you! - Jul 16th 2009, 03:13 AMalexmahone
$\displaystyle h(x)=5-2^x$

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

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$\displaystyle 2^x>0$

$\displaystyle -2^x<0$

$\displaystyle 5-2^x<5$

The range for $\displaystyle h(x) = 5 - 2^x$ is $\displaystyle (-\infty, 5).$ - Jul 16th 2009, 03:15 AMyeongil
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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