https://file.aiquickdraw.com/mathbot/file/1727927808078lpld4xh3.jpg

Let's analyze the graph and answer the questions.

1. **Domain of the function**:
   The function has a vertical asymptote at \(x = 1\) (as indicated by the dashed red line). The function is undefined at \(x = 1\) but is defined for all other values of \(x\). Therefore, the domain of the function is:
   \[
   (-\infty, 1) \cup (1, \infty)
   \]

2. **Equation of the vertical asymptote**:
   The vertical asymptote occurs where the function approaches infinity or negative infinity, which happens at \(x = 1\). Therefore, the equation of the vertical asymptote is:
   \[
   x = 1
   \]

3. **Equation of the horizontal asymptote**:
   As \(x\) approaches very large positive or negative values, the function seems to approach \(y = 0\). Thus, the equation of the horizontal asymptote is:
   \[
   y = 0
   \]

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Here are five related questions to extend your understanding:
1. What type of function usually has a vertical asymptote?
2. How can you find vertical asymptotes algebraically for rational functions?
3. What happens to the function's values as \(x\) approaches the vertical asymptote from the left or right?
4. Can a function have more than one vertical or horizontal asymptote?
5. How do vertical and horizontal asymptotes help in sketching the graph of a function?

**Tip**: Vertical asymptotes typically occur where the denominator of a rational function equals zero, provided it doesn't cancel with the numerator.

Consider the function graphed above. 1. Select the domain of the function. 2. Give the equation of the vertical asymptote. 3. Give the equation of the horizontal asymptote.

Analyze the graph of a rational function with a vertical asymptote at x=1 and a horizontal asymptote at y=0. Learn how to determine the domain and the equations of the asymptotes in this problem, suitable for Grades 10-12.

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