In the context of a step function, closed circles and open circles are used to represent the function’s value at particular points on the graph.
A closed circle indicates that the value at that point is included in the function. This means that if the step function has a closed circle at a given x-value, the corresponding y-value is part of the function. For example, if a point is represented as (a, b) with a closed circle, it signifies that f(a) = b.
On the other hand, an open circle signifies that the value at that point is not included in the function. Using the same notation, if there is an open circle at (a, b), it indicates that f(a) ≠ b, meaning the function does not take the value b at x = a.
These graphical representations help us understand the behavior of step functions, especially when there are jumps or discontinuities in the function’s values. Closed circles are often found at the endpoints of intervals where the function takes a specific constant value, while open circles may appear where the function jumps to a different constant value.