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

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