Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of $$ y=f(x) $$. $$ f(x)=e^{0.5 x}+324 e^{-0.5 x} $$ A. The domain of $$ f $$ is $$ (-\infty, \infty) $$. The domain of $$ f $$ is empty. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $$ x $$-intercept(s) of $$ f $$ is $$ x= $$ (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) B. The function $$ f $$ has no $$ x $$-intercepts. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $$ y $$-intercept of $$ f $$ is $$ y=\square $$. B. The function $$ f $$ has no to separate answers as needed.) (Type an exact answer, using radicals as needed.)

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To analyze the function $$ f(x) = e^{0.5x} + 324e^{-0.5x} $$, we will follow these steps:

1. **Determine the domain of $$ f $$**:
   - The function $$ f(x) $$ is composed of exponential functions, which are defined for all real numbers. Therefore, the domain of $$ f $$ is $$ (-\infty, \infty) $$.

2. **Find the $$ x $$-intercepts**:
   - To find the $$ x $$-intercepts, we set $$ f(x) = 0 $$:
   $$
   e^{0.5x} + 324e^{-0.5x} = 0
   $$
   - Rearranging gives:
   $$
   e^{0.5x} = -324e^{-0.5x}
   $$
   - Since $$ e^{0.5x} $$ is always positive and $$ -324e^{-0.5x} $$ is always negative, there are no solutions to this equation. Thus, the function $$ f $$ has no $$ x $$-intercepts.

3. **Find the $$ y $$-intercept**:
   - To find the $$ y $$-intercept, we evaluate $$ f(0) $$:
   $$
   f(0) = e^{0.5 \cdot 0} + 324e^{-0.5 \cdot 0} = 1 + 324 = 325
   $$
   - Therefore, the $$ y $$-intercept of $$ f $$ is $$ y = 325 $$.

Now, let's summarize the findings:

- **Domain**: $$ (-\infty, \infty) $$
- **$$ x $$-intercepts**: The function $$ f $$ has no $$ x $$-intercepts.
- **$$ y $$-intercept**: $$ y = 325 $$

Next, I will sketch the graph of $$ f(x) $$.

### Sketch of the Graph of $$ f(x) $$

The function $$ f(x) = e^{0.5x} + 324e^{-0.5x} $$ will have the following characteristics:
- As $$ x \to -\infty $$, $$ e^{0.5x} \to 0 $$ and $$ 324e^{-0.5x} \to \infty $$, so $$ f(x) \to \infty $$.
- As $$ x \to \infty $$, $$ e^{0.5x} \to \infty $$ and $$ 324e^{-0.5x} \to 0 $$, so $$ f(x) \to \infty $$.
- The function is continuous and has a minimum point since it approaches infinity in both directions.

Now, I will summarize the results in the required format:

### Summary
A. The domain of $$ f $$ is $$ (-\infty, \infty) $$.

B. The $$ x $$-intercept(s) of $$ f $$ is: **B. The function $$ f $$ has no $$ x $$-intercepts.**

C. The $$ y $$-intercept of $$ f $$ is $$ y = 325 $$.
A. The domain of $$ f $$ is $$ (-\infty, \infty) $$. B. The function $$ f $$ has no $$ x $$-intercepts. C. The $$ y $$-intercept of $$ f $$ is $$ y = 325 $$.

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