c. $$ \frac{-11}{x}, \frac{7}{x-4}, \frac{x}{x^{2}-16} $$

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It looks like you've provided three rational functions:

c. $$ \frac{-11}{x} $$, $$ \frac{7}{x-4} $$, $$ \frac{x}{x^{2}-16} $$

To analyze these functions, let's explore their **domains**, **vertical asymptotes**, and **horizontal asymptotes**.

---

### 1. $$ \frac{-11}{x} $$

**Domain:**
- The denominator $$ x $$ cannot be zero.
- **Domain:** $$ x 
eq 0 $$

**Vertical Asymptote:**
- Occurs where the denominator is zero.
- $$ x = 0 $$

**Horizontal Asymptote:**
- Compare the degrees of the numerator and denominator.
- Both numerator and denominator are degree 1.
- The horizontal asymptote is the ratio of the leading coefficients: $$ y = \frac{-11}{1} = -11 $$

**Summary:**
- **Domain:** $$ x 
eq 0 $$
- **Vertical Asymptote:** $$ x = 0 $$
- **Horizontal Asymptote:** $$ y = -11 $$

---

### 2. $$ \frac{7}{x-4} $$

**Domain:**
- The denominator $$ x - 4 $$ cannot be zero.
- **Domain:** $$ x 
eq 4 $$

**Vertical Asymptote:**
- Occurs where the denominator is zero.
- $$ x = 4 $$

**Horizontal Asymptote:**
- The degrees of the numerator and denominator are both 1.
- The horizontal asymptote is the ratio of the leading coefficients: $$ y = \frac{7}{1} = 7 $$

**Summary:**
- **Domain:** $$ x 
eq 4 $$
- **Vertical Asymptote:** $$ x = 4 $$
- **Horizontal Asymptote:** $$ y = 7 $$

---

### 3. $$ \frac{x}{x^{2}-16} $$

First, factor the denominator:

$$ x^{2} - 16 = (x - 4)(x + 4) $$

So, the function becomes:

$$ \frac{x}{(x - 4)(x + 4)} $$

**Domain:**
- The denominator $$ (x - 4)(x + 4) $$ cannot be zero.
- $$ x 
eq 4 $$ and $$ x 
eq -4 $$
- **Domain:** $$ x \in \mathbb{R} $$, $$ x 
eq \pm 4 $$

**Vertical Asymptotes:**
- Occur where the denominator is zero.
- $$ x = 4 $$ and $$ x = -4 $$

**Horizontal Asymptote:**
- Compare the degrees of the numerator and denominator.
- Numerator degree: 1
- Denominator degree: 2
- Since the denominator has a higher degree, the horizontal asymptote is $$ y = 0 $$

**Summary:**
- **Domain:** $$ x 
eq \pm 4 $$
- **Vertical Asymptotes:** $$ x = 4 $$ and $$ x = -4 $$
- **Horizontal Asymptote:** $$ y = 0 $$

---

### Visual Representation

To better understand these functions, graphing them can be helpful. Here's a brief description of their graphs:

1. **$$ \frac{-11}{x} $$:**
   - Hyperbola with branches in the second and fourth quadrants.
   - Approaches $$ x = 0 $$ vertically and $$ y = -11 $$ horizontally.

2. **$$ \frac{7}{x-4} $$:**
   - Hyperbola shifted right by 4 units.
   - Approaches $$ x = 4 $$ vertically and $$ y = 7 $$ horizontally.

3. **$$ \frac{x}{x^{2}-16} $$:**
   - More complex hyperbola with vertical asymptotes at $$ x = 4 $$ and $$ x = -4 $$.
   - Approaches $$ y = 0 $$ horizontally.

---

### Additional Considerations

- **Intercepts:**
  - **Y-Intercept:** Set $$ x = 0 $$ and solve for $$ y $$ (if within the domain).
  - **X-Intercept:** Set $$ y = 0 $$ and solve for $$ x $$.

- **Behavior Near Asymptotes:**
  - Analyze the limits as $$ x $$ approaches the vertical asymptotes from the left and right.

- **Symmetry:**
  - Determine if the functions are even, odd, or neither.

If you have a specific question or need further analysis on these functions, feel free to ask!
The three rational functions are: 1. $$ \frac{-11}{x} $$ with a vertical asymptote at $$ x = 0 $$ and a horizontal asymptote at $$ y = -11 $$. 2. $$ \frac{7}{x-4} $$ with vertical asymptotes at $$ x = 4 $$ and a horizontal asymptote at $$ y = 7 $$. 3. $$ \frac{x}{x^{2}-16} $$ with vertical asymptotes at $$ x = 4 $$ and $$ x = -4 $$, and a horizontal asymptote at $$ y = 0 $$.

c. \( \frac{-11}{x}, \frac{7}{x-4}, \frac{x}{x^{2}-16} \)

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