https://file.aiquickdraw.com/mathbot/file/1725797802039aounuxq9.jpg

The image contains four functions for which you are asked to construct a table of values and sketch their graphs. The functions are:

1. \( f(x) = \frac{1}{x} \)
2. \( F(x) = \frac{1}{x - 2} \)
3. \( g(x) = \frac{x}{x + 1} \)
4. \( G(x) = \frac{2}{(x - 2)^2} \)

### To proceed:

1. **Construct a table of values**: For each function, choose a set of values for \(x\), calculate the corresponding \(y = f(x)\), and then create a table of the points.
2. **Sketch the graph**: Plot the points on a coordinate system and draw the curve for each function based on their behavior (e.g., asymptotes, intercepts).

Would you like me to compute the table of values for a specific function or for all of them?

Construct a table of values and sketch the graph of the following functions: f(x) = 1/x, F(x) = 1/(x - 2), g(x) = x/(x + 1), G(x) = 2/(x - 2)^2.

Learn how to construct tables of values and sketch the graphs of rational functions, including f(x) = 1/x and F(x) = 1/(x - 2). This tutorial covers key mathematical concepts such as vertical and horizontal asymptotes and graphing rational functions. Suitable for high school students.

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