Here is the graph of the function $f(x) = \frac{1}{x}$. You can observe that:

• The graph consists of two branches, located in the first and third quadrants.
• It has vertical and horizontal asymptotes at $x = 0$ and $y = 0$, respectively.

Summary:

• Domain: $x \in (-\infty, 0) \cup (0, +\infty)$
• Range: $y \in (-\infty, 0) \cup (0, +\infty)$

Would you like more details or have any questions?

Related Questions:

1. What are asymptotes, and how are they determined for a given function?
2. How does the graph of $f(x) = \frac{1}{x}$ compare to $f(x) = \frac{1}{x^2}$?
3. What are the transformations of $f(x) = \frac{1}{x}$ when it is translated or scaled?
4. How can we find the inverse of the function $f(x) = \frac{1}{x}$, and what does its graph look like?
5. What is the behavior of the function $f(x) = \frac{1}{x}$ as $x \to \infty$ or $x \to -\infty$?

Tip: For functions involving division by zero, always consider the behavior near the undefined points to understand their graph better.