Hyperbolic or S- shaped (sigmoid) curve with the sharp transition from low to high reaction rate over a narrow range of substrate concentration.

Introduction:
The Michaelis-Menten approach is a mathematical model that describes the kinetics of enzyme-catalyzed reactions. It provides insights into the relationship between the initial velocity (V) of the reaction and the substrate concentration (S). The graph obtained from this approach allows us to understand the enzyme-substrate interaction and the behavior of the reaction.

Explanation:
The graph between initial velocity (V) and substrate concentration (S) according to the Michaelis-Menten approach is a hyperbolic curve (option C). This curve is also known as the Michaelis-Menten plot or the saturation curve.

Key Points:
Here are the key points explaining why the graph is a hyperbolic curve:

1. Saturation: As the substrate concentration increases, the initial velocity of the reaction also increases. However, at high substrate concentrations, the enzyme becomes saturated with substrates, and the reaction rate plateaus. This results in a curve that levels off at the maximum velocity (Vmax) of the reaction.

2. Active site occupancy: The hyperbolic curve represents the occupancy of the active sites on the enzyme by the substrate molecules. Initially, when the substrate concentration is low, there are many available active sites for substrate binding, resulting in a steep increase in velocity. As the substrate concentration increases, the active sites become occupied, and the rate of velocity increase slows down.

3. Michaelis constant: The curve is defined by a parameter called the Michaelis constant (Km), which represents the substrate concentration at which the reaction rate is half of the maximum velocity. Km reflects the affinity of the enzyme for the substrate. The lower the Km value, the higher the affinity of the enzyme for the substrate.

4. Shape: The hyperbolic shape of the curve indicates that the reaction rate becomes less sensitive to changes in substrate concentration at high concentrations. At low substrate concentrations, even a small increase in substrate concentration leads to a significant change in reaction rate.

Conclusion:
According to the Michaelis-Menten approach, the graph between initial velocity (V) and substrate concentration (S) of an enzyme-catalyzed reaction is a hyperbolic curve. This curve represents the saturation of enzyme active sites and the relationship between substrate concentration and reaction velocity.