Identify the horizontal asymptote of the function $$ f(x) = 3 e^{-x} + 5 $$.

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To identify the horizontal asymptote of the function $$ f(x) = 3 e^{-x} + 5 $$, we analyze the behavior of the function as $$ x $$ approaches both $$ +\infty $$ and $$ -\infty $$.

1. **As $$ x \to +\infty $$:**
   $$
   e^{-x} \to 0
   $$
   Therefore,
   $$
   f(x) = 3 e^{-x} + 5 \to 3(0) + 5 = 5
   $$

2. **As $$ x \to -\infty $$:**
   $$
   e^{-x} \to +\infty
   $$
   Therefore,
   $$
   f(x) = 3 e^{-x} + 5 \to 3(+\infty) + 5 = +\infty
   $$

From this analysis, we can see that as $$ x $$ approaches $$ +\infty $$, the function approaches the constant value $$ 5 $$. However, as $$ x $$ approaches $$ -\infty $$, the function grows without bound.

**Conclusion:**
The horizontal asymptote of the function $$ f(x) = 3 e^{-x} + 5 $$ is the horizontal line $$ y = 5 $$.

**Answer:** 
Its horizontal asymptote is the line y = 5.
The horizontal asymptote of the function $$ f(x) = 3 e^{-x} + 5 $$ is $$ y = 5 $$.

Identify the horizontal asymptote of the function .

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