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What is the end behavior of $f(x)=2^{-x}+5$ as $x$ goes to infinity?
$f(x)$ goes to 5
$f(x)$ goes to -10
$f(x)$ goes to infinity
$f(x)$ goes to negative infinity
$f(x)$ goes to 0
Answer
Final Answer: $\boxed{f(x) \text{ goes to } 5}$
Step 1 ：The function $f(x)=2^{-x}+5$ is a transformation of the function $y=2^{-x}$, which is an exponential decay function.
Step 2 ：As $x$ goes to infinity, $2^{-x}$ goes to 0.
Step 3 ：Therefore, $f(x)$ goes to $0+5=5$.
Step 4 ：We can confirm this by plotting the function.
Step 5 ：The plot confirms that as $x$ goes to infinity, $f(x)$ approaches 5.
Step 6 ：Therefore, the end behavior of $f(x)=2^{-x}+5$ as $x$ goes to infinity is that $f(x)$ goes to 5.
Step 7 ：Final Answer: $\boxed{f(x) \text{ goes to } 5}$
