To graph the equation \( y = \frac{5}{x} \), we'll need to consider its key features, including asymptotes, intercepts, and general shape.

### Key Features:

1. **Asymptotes:**
   - **Vertical Asymptote:** \( x = 0 \) (since \( y \) becomes undefined at \( x = 0 \)).
   - **Horizontal Asymptote:** \( y = 0 \) (as \( x \) approaches infinity, \( y \) approaches 0).

2. **Intercepts:**
   - **No x-intercept** (the graph never crosses the x-axis since \( y \) never equals 0).
   - **y-intercept:** There is no y-intercept because the function is undefined at \( x = 0 \).

3. **Shape:**
   - The graph is a hyperbola with two branches:
     - For \( x > 0 \), \( y \) is positive, and the curve lies in the first quadrant.
     - For \( x < 0 \), \( y \) is negative, and the curve lies in the third quadrant.

### Graph:
- As \( x \) increases, \( y \) decreases approaching 0 from above.
- As \( x \) decreases (negative), \( y \) increases in magnitude, approaching 0 from below.

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Explore the graph of y = 5/x with detailed explanations of asymptotes, intercepts, and its hyperbolic shape. This mathematical problem involves graphing techniques and understanding the behavior of functions around asymptotes. Suitable for Grades 10-12 students and math enthusiasts.

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