How can the performance of a given pump be changed?

The performance of a pump can certainly be altered by changing the speed at the impeller edge. The impeller is a critical component of the pump that imparts energy to the fluid, and its rotational speed directly affects the flow rate and pressure of the fluid being pumped. Increasing the speed typically results in a higher flow rate and increased pressure, while reducing the speed will decrease both.

Adjusting the valve settings and decreasing water temperature can have some impact on the overall system, but they do not modify the pump's inherent performance parameters in the same direct manner as altering the impeller speed. Valve adjustments primarily control flow and pressure in the system but do not change the pump's capacity or efficiency. Lowering the water temperature can affect its viscosity and density, which might influence performance to a degree, but again, this is not a direct modification to the pump's operating characteristics.

Thus, focusing on the speed at the impeller edge provides a clear and effective method to change the pump's performance directly, making it the most relevant factor among the options provided.