The graph shown in the image represents the function $f(x) = \frac{1}{x}$. Here's why:

• The graph exhibits two distinct branches, one in the first quadrant and the other in the third quadrant, separated by asymptotes at $x = 0$ (vertical asymptote) and $y = 0$ (horizontal asymptote).
• This behavior aligns with the reciprocal function $f(x) = \frac{1}{x}$.

Let me know if you'd like further clarification!

Here are five related questions to expand your understanding:

1. What is the domain and range of the function $f(x) = \frac{1}{x}$?
2. How do vertical and horizontal asymptotes affect graph behavior?
3. How does the graph of $f(x) = \frac{1}{x}$ change with transformations like $f(x) = \frac{1}{x+1}$?
4. How does $f(x) = \frac{1}{x}$ compare to $f(x) = \frac{1}{x^2}$ in terms of shape and symmetry?
5. What are real-world applications of reciprocal functions?

Tip: When identifying functions by their graphs, focus on key features like symmetry, asymptotes, and the overall shape!