Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of $$ \mathrm{f}(\mathrm{x})=\frac{\mathrm{x}+9}{\mathrm{x}-9} $$. Find the y-intercepts of $$ \mathrm{f}(\mathrm{x}) $$. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $$ y $$-intercept(s) is/are at $$ \mathrm{y}= $$ (Type an integer or a decimal. Use a comma to separate answers as needed.) B. There are no y-intercepts. Find any horizontal asymptotes of $$ \mathrm{f}(\mathrm{x}) $$. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one horizontal asymptote, $$ \square $$. (Type an equation.) B. The function has two horizontal asymptotes. The top asymptote is $$ \square $$ and the bottom asymptote is (Type equations.) C. There are no horizontal asymptotes.

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To analyze the function $$ f(x) = \frac{x + 9}{x - 9} $$, we will follow these steps:

### Step 1: Find the y-intercepts
The y-intercept occurs when $$ x = 0 $$. We can find it by substituting $$ x = 0 $$ into the function:

$$
f(0) = \frac{0 + 9}{0 - 9} = \frac{9}{-9} = -1
$$

Thus, the y-intercept is at $$ y = -1 $$.

### Step 2: Determine horizontal asymptotes
To find horizontal asymptotes, we analyze the behavior of $$ f(x) $$ as $$ x $$ approaches infinity or negative infinity.

For large values of $$ x $$:

$$
f(x) = \frac{x + 9}{x - 9} \approx \frac{x}{x} = 1
$$

Thus, as $$ x \to \infty $$ or $$ x \to -\infty $$, $$ f(x) $$ approaches 1. Therefore, there is one horizontal asymptote at $$ y = 1 $$.

### Summary of Findings
- **Y-intercept**: The y-intercept is at $$ y = -1 $$.
- **Horizontal asymptote**: The function has one horizontal asymptote at $$ y = 1 $$.

### Final Answers
1. **Y-intercept**: 
   - A. The $$ y $$-intercept(s) is/are at $$ y = -1 $$.

2. **Horizontal asymptotes**: 
   - A. The function has one horizontal asymptote, $$ y = 1 $$.

### Sketch of the Graph
The graph of $$ f(x) = \frac{x + 9}{x - 9} $$ will have the following characteristics:
- A vertical asymptote at $$ x = 9 $$ (where the denominator is zero).
- A horizontal asymptote at $$ y = 1 $$.
- A y-intercept at $$ (0, -1) $$.

The graph will approach the horizontal asymptote as $$ x $$ goes to positive and negative infinity, and it will diverge to positive or negative infinity as it approaches the vertical asymptote at $$ x = 9 $$.

The sketch would show these features clearly, with the curve approaching the asymptotes and crossing the y-axis at $$ -1 $$.
- **Y-intercept**: $$ y = -1 $$ - **Horizontal asymptote**: $$ y = 1 $$

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