https://file.aiquickdraw.com/mathbot/file/17267858618163a9iqhxp.jpg

Let's analyze the given graph and answer the questions one by one.

### (a) Domain and Range:
- **Domain**: The graph has vertical asymptotes at \(x = -6\) and \(x = 6\), meaning the function is undefined at these points. Hence, the domain excludes these points. The domain is:
  \[
  \text{Domain} = (-\infty, -6) \cup (-6, 6) \cup (6, \infty)
  \]

- **Range**: From the graph, it appears that the function's range excludes \(y = 0\). The function tends to infinity as \(y\) approaches large positive or negative values. The range is:
  \[
  \text{Range} = (-\infty, 0) \cup (0, \infty)
  \]

### (b) Intercepts:
- **x-intercepts**: There are no points where the graph crosses the \(x\)-axis, meaning there are no x-intercepts.
- **y-intercept**: The graph crosses the \(y\)-axis at \(y = -2\), so the y-intercept is:
  \[
  \text{y-intercept} = (0, -2)
  \]

### (c) Horizontal Asymptotes:
The graph approaches \(y = 0\) as \(x\) tends to \(\pm \infty\), indicating a horizontal asymptote at:
  \[
  y = 0
  \]

### (d) Vertical Asymptotes:
From the graph, the vertical asymptotes occur where the function becomes undefined, at \(x = -6\) and \(x = 6\). Therefore, the vertical asymptotes are:
  \[
  x = -6 \quad \text{and} \quad x = 6
  \]

### (e) Oblique Asymptotes:
Oblique asymptotes occur when the function behaves like a slanting line at extreme values of \(x\). From the graph, there are no signs of oblique asymptotes because the function has horizontal asymptotes at \(y = 0\), not slanted lines. Hence:
  \[
  \text{No oblique asymptotes.}
  \]

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Would you like more details or have any questions? 

Here are some related questions to consider:
1. How do we calculate the equation of a horizontal asymptote from a function?
2. Can vertical asymptotes appear in functions like rational functions? How are they identified?
3. What conditions lead to the existence of oblique asymptotes in rational functions?
4. How would adding shifts or transformations affect the intercepts and asymptotes?
5. How does the concept of limits help in understanding asymptotic behavior?

**Tip**: To determine vertical asymptotes for a rational function, analyze where the denominator equals zero, as this is where the function tends to infinity.

Use the graph shown to find the following: (a) The domain and range of the function (b) The intercepts, if any (c) Horizontal asymptotes, if any (d) Vertical asymptotes, if any (e) Oblique asymptotes, if any

Explore how to determine the domain, range, intercepts, and asymptotes (horizontal, vertical, and oblique) using the given function graph. This problem covers advanced concepts such as vertical asymptotes at x = -6 and x = 6, a horizontal asymptote at y = 0, and no oblique asymptotes.

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