Final answer:
The question pertains to the properties of a polynomial function including local extrema, critical and inflection points, absolute extrema, and the domain and range, all of which are key concepts in high school mathematics, particularly calculus.
Step-by-step explanation:
The subject of the question concerns the polynomial function and its properties related to calculus, specifically focusing on:
- Local Maxima and Local Minima - These are points where the function reaches a local highest or lowest value, respectively.
- Critical Points and Inflection Points - Critical points are where the derivative equals zero or is undefined, and inflection points are where the second derivative changes sign, indicating a change in concavity.
- Absolute Maximum and Absolute Minimum - The highest or lowest value that a function takes on an interval or the entire domain.
- Domain and Range - The set of all possible input values (the domain) and all possible output values (the range) of a function.
To explore these characteristics, one may use a variety of tools, including calculus techniques and graphing calculators, to analyze the behaviour of polynomial functions graphically and numerically.