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1. The function \( f(x) = \frac{1}{x-1} \) is defined for all \( x \neq 1 \). It has a vertical asymptote at \( x = 1 \) since the function becomes undefined at this point.

2. The function \( f(x) = x + 2 \) is a linear function with a slope of 1 and a y-intercept at \( (0,2) \). It is defined for all real numbers \( x \).

3. The function \( f(x) = 3 \) is a constant function. It is horizontal and has the same output, 3, for all inputs \( x \). It is also defined for all real numbers \( x \).

4. The function \( f(x) = \frac{1}{x-1} \) was revisited to find the domain, which is all real numbers except \( x = 1 \).

5. The second question appears to ask for the evaluation of different functions:
   - \( f(x) = \frac{1}{x-1} \)
   - \( f(x) = x+2 \)
   - \( f(x) = 3 \)

   The specific values of \( x \) to substitute into these functions are not visible, but you might be asking for evaluation at specific points.

Please clarify if there are specific values of \( x \) for which you need these functions evaluated, or if there are other questions you need help with!

Would you like more detailed explanations on any of these points? If you have any further questions or if there's anything specific you'd like to explore, please let me know!

### Related Questions
1. How would you graph the function \( f(x) = \frac{1}{x-1} \)?
2. What are the implications of the slope and y-intercept of the function \( f(x) = x+2 \)?
3. How does the graph of a constant function like \( f(x) = 3 \) look?
4. What is the importance of knowing the domain of a function in calculus?
5. How do you find the inverse of a function like \( f(x) = x+2 \)?

**Tip:** Remember, the domain of a function is all the values of \( x \) for which the function is mathematically defined. Identifying vertical asymptotes and holes is crucial for understanding the behavior of rational functions.

1. Hallar la ecuación de la recta que satisfaga los siguientes datos para el punto P(3, 0) y la pendiente de la recta (m): f(x) = x + 2; f(x) = 3; f(x) = 5x^2 - 1; a = 1. 
2. Calcular los dominios de las siguientes funciones con el punto de la división: f(x) = a/(x-1).

Learn how to calculate the domain of different functions such as f(x) = x + 2 and f(x) = 5x^2 - 1. Solve for specific points using the point-slope form and linear function principles. Suitable for students in Grade 10-12.

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