How do I find the Domain and Range of the function
h(x)=5−2ˆ(x)
Thank you!
$\displaystyle h(x)=5-2^x$
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 $\displaystyle (-\infty, 5).$
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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