Question

what do the closed and open circles on the graph of a step function indicate? closed and open circles are used to indicate which part of the domain includes the ends of the steps. a closed circle indicates that the x - value is that part of the domain, and an open circle indicates that the point is that part of the domain.

Explanation:

In the context of a step - function graph, closed circles are used to show inclusion of an \(x\) - value in a particular part of the domain. Open circles are used to show exclusion of a point from a particular part of the domain. This is based on the standard notation in graphing piece - wise functions (of which step functions are a type). For example, if we have a step function \(y = f(x)\) defined as \(y = 1\) for \(0\leq x<1\) and \(y = 2\) for \(1\leq x < 2\), at \(x = 1\) for the first part of the function (\(y = 1\)), we use an open circle (because \(x = 1\) is not included in the domain \(0\leq x<1\)), and for the second part (\(y=2\)) we use a closed circle (because \(x = 1\) is included in the domain \(1\leq x < 2\)).

Answer:

A closed circle indicates that the \(x\) - value is included in that part of the domain, and an open circle indicates that the point is not included in that part of the domain.