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What are characteristics of the graph of the reciprocal parent function?
It is a hyperbola, it is in quadrants I and II
Difference between controllers and compensators in control system?
A compensator is a controller meant to improve characteristics of the open-loop plant so that it can safely be used with feedback control. For example, there is a (parasitic) feedback system in a commercial audio system (e.g., in a theater) formed from a microphone, the soundboard connected to it, and the speakers in the theater connected to the soundboard. If the microphone is positioned in certain locations near the speakers and there is enough gain in the system, a single tone (and possibly its higher harmonics) can be reinforced by the feedback system causing it to grow and grow until it is deafeningly loud. It is then the sound engineers' job to "compensate" this system at the soundboard by adjusting the system's gain and phase characteristics around that particular frequency. So here, the soundboard is certainly a controller (compensation is a control topic), but the controller is not responsible for tracking or regulation. Instead, it is enforcing stability of the closed-loop system at all frequencies.
What are the characteristics of futures?
Futurism developed to glorify the urban life as well as machinery/industrialization. Futurism employs techniques of Divisionism (see Seurat's artwork!), Cubism features (specifically the analysis of energy), dynamism, urban subject matters, and depiction of movement. If you look at Umberto Boccioni's Unique Forms of Continuity in Space and also his The City Rises painting, you will get a pretty good idea of Futurism!
What does droop mean?
In the context of electrical engineering, "droop" refers to a reduction in voltage or current levels due to an increase in load or demand on a power system. Droop control is a method used in power systems to regulate and maintain stable voltage levels by adjusting the output of generators in response to changes in load. Droop characteristics are defined by the amount of voltage or frequency deviation from the nominal value as a function of the load current.
Are graphs useful for describing functions?
YES! Simply by taking a quick glance at a graph, you can see several characteristics of the function: local minimums/maximums, points of inflection, end behavior, asymptotes, etc etc... If you wanted to find these without the graph, you would have to do some math which might end up being very time consuming for very complicated functions. Even worse: what if the function is not elementary, and you can't express it in terms of finite arithmetic operations?
