CoreProRational Functions
Reciprocal
f(x) = 1/x
Overview
The reciprocal function has a vertical asymptote at x=0 and a horizontal asymptote at y=0.
Domain
(-∞, 0) ∪ (0, +∞)
Range
(-∞, 0) ∪ (0, +∞)
Symmetry
Odd
Key Properties
1
Vertical asymptote: x = 0
2
Horizontal asymptote: y = 0
3
Odd function
4
Hyperbola shape
Key Insight
As x → 0⁺, f(x) → +∞. As x → 0⁻, f(x) → -∞. The function "blows up" near zero.
Visualize Reciprocal
Interact with the graph, adjust parameters, and see how the function behaves in real time.