Select your answer (21 out of 25) 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

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: $\boxed{f(x) \text{ goes to } 5}$