Final answer:
The end behavior of a function refers to how the y-values of the function behave as x approaches very large positive or negative values, shedding light on the function's behavior on the far right or left of the graph.
Step-by-step explanation:
The end behavior of a function pertains to the characteristic described by option A: 'The value of the function for large and small values of x'. When graphing a function, the end behavior can be visualized by looking at what happens to the y values as x approaches very large positive values (often described as x approaching infinity) or very large negative values (x approaching negative infinity). For example, the function y = 1/x has an interesting end behavior; as x approaches infinity, y approaches zero, and as x approaches negative infinity, y also approaches zero, illustrating the concept of horizontal asymptote.
End behavior does not refer to the largest and smallest y values (option B), which are called extrema, or to y values that repeat at regular intervals of x (option C), which describes periodic behavior. Instead, it is all about the trends of the function's graph far to the right or left along the x-axis.
As an example, let's consider the quadratic function f(x) = x². As x becomes very large or very small, the y values become very large since squaring any large number results in an even larger positive number. This tells us about the end behavior of a parabola opening upwards.