Final answer:
The end behavior of the function f(x) = 2x⁶ - 2x² - 5 is that as x approaches positive or negative infinity, f(x) goes to positive infinity, causing both tails of the graph to point upwards.
Step-by-step explanation:
To determine the end behavior of the graph of the function f(x) = 2x⁶ - 2x² - 5, we need to analyze the leading term, which is 2x⁶. Since the exponent of the leading term is even (6) and the leading coefficient (2) is positive, the end behavior of the graph will be such that as x approaches positive or negative infinity, the f(x) value goes to positive infinity.
This means that both tails of the graph will point upwards. Understanding end behavior and equation grapher tools can help to visualize this concept. It is not necessary to shade any part of the graph for this particular function as it relates only to the end behavior, and not an inequality.
The graph would not exactly mirror the descriptions related to the sample frequency graph, falling objects, or the book's motion graphs from the given context, as these are specific use-cases and do not directly apply to polynomial end behavior analysis.