The graph above illustrates the reciprocal function $f(x) = \frac{1}{x}$:

• The vertical asymptote (red dashed line) is at $x = 0$, where the function is undefined.
• The horizontal asymptote (green dashed line) is at $y = 0$, where the function approaches zero as $x$ becomes very large or very small.

Summary of Steps:

1. Identify key points on the graph, such as $f(1) = 1$ and $f(-1) = -1$.
2. Draw the vertical asymptote at $x = 0$ and the horizontal asymptote at $y = 0$.
3. Sketch the curve, ensuring that the function gets very large near $x = 0$ and approaches zero for large $x$ values.

Would you like any further details, or do you have questions?

Here are 5 related questions for you:

1. How does the reciprocal function change when a constant is added?
2. What happens to the graph of $f(x) = \frac{1}{x}$ if the reciprocal is squared?
3. How do reciprocal functions relate to hyperbolas?
4. Can you give an example of a real-world application of reciprocal functions?
5. How do you find the inverse of a reciprocal function?

Tip: When graphing functions, understanding asymptotes helps predict the behavior at critical points.