Below is the graph of a rectangular hyperbola:

The graph shows two distinct curves that approach vertical and horizontal asymptotes. This shape is characteristic of a hyperbola. The problem explicitly states it is a "rectangular hyperbola".

• 1.1. $y = ab^x + q, b > 0$: This is the general form of an exponential function. Its graph is a curve that increases or decreases rapidly, approaching a horizontal asymptote. This does not match the given graph.
• 1.2. $y = ax + q$: This is the general form of a linear function. Its graph is a straight line. This does not match the given graph.
• 1.3. $y = ax^2 + q$: This is the general form of a quadratic function. Its graph is a parabola (U-shaped curve). This does not match the given graph.
• 1.4. $y = \frac{a}{x} + q; a \neq 0$: This is the general form of a rectangular hyperbola. Its graph consists of two branches, with vertical and horizontal asymptotes. This matches the description and the visual representation of the given graph.

Based on the analysis, the equation that represents a rectangular hyperbola is $y = \frac{a}{x} + q$.

The correct equation is 1.4.