The function \( h(x) = \left| \frac{1}{x} \right| \) represents the absolute value of the reciprocal function. Let's analyze and describe its key characteristics to understand its graph:

### Key characteristics of \( h(x) = \left| \frac{1}{x} \right| \):
1. **Domain**: The function is undefined at \( x = 0 \) because division by zero is not possible. Therefore, the domain is \( (-\infty, 0) \cup (0, \infty) \).
2. **Range**: Since we are taking the absolute value, the output is always positive. The range is \( (0, \infty) \).
3. **Asymptotes**:
   - **Vertical Asymptote**: At \( x = 0 \), the function approaches infinity as \( x \) gets closer to zero from either side. Hence, there is a vertical asymptote at \( x = 0 \).
   - **Horizontal Asymptote**: As \( |x| \) increases (either positively

Explore the graph of the function h(x) = |1/x|, focusing on its domain, range, and asymptotic behavior. Learn how this function behaves around vertical and horizontal asymptotes. Ideal for high school students studying algebra and functions.

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