A reciprocal function is of the form $f(x) = \frac{1}{x}$. The graph of this function is characterized by two distinct branches: one in the first quadrant (where both $x > 0$ and $y > 0$) and another in the third quadrant (where both $x < 0$ and $y < 0$).

Here are some key features of the graph of the reciprocal function $f(x) = \frac{1}{x}$:

• The graph has vertical and horizontal asymptotes:

  • Vertical Asymptote: At $x = 0$, because the function is undefined when $x = 0$.
  • Horizontal Asymptote: At $y = 0$, as the function approaches 0 when $x \to \infty$ or $x \to -\infty$.

• The graph is a hyperbola.

Would you like me to generate a graph for this function, or do you have specific details you'd like to explore?