# Math Help - Domain and Range of h(x)=5−2ˆ(x)?

1. ## Domain 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!

2. $h(x)=5-2^x$

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

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$2^x>0$

$-2^x<0$

$5-2^x<5$

The range for $h(x) = 5 - 2^x$ is $(-\infty, 5).$

3. Originally Posted by Polyxendi
How do I find the Domain and Range of the function

h(x)=5−2ˆ(x)

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

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

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