Graph Of Step Functions

Question

If we are asked to graph the step function $[\sqrt{x}]$ for $0 \leq x \leq 10$, I have seen a solution, which is given below,

what I am having doubts about is the closed circle at the end when $x=10$, if I were to graph it, it would be an open circle. Am I missing something here? Is there any cases where we have two closed circles in a step function graph?

Another question was to graph the step function $[x+\dfrac{1}{2}]$ on the interval $[-2,2]$, the solution is given as

shouldn't this also be an open circle at the end when $x=2$?

Answer 1

Both filled circles indicate that the corresponding point belongs to the graph:

• $x = 10$ is in the domain and $[\sqrt{10}] = 3$
• $x = 2$ is in the domain and $[2+\frac{1}{2}] = 2$

The empty circles indicate that the corresponding point does not belong to the graph.