If all points of the step function $f(x) = \lceil 2x \rceil - 1$ are graphed, then the domain of $f(x)$ would be the set of $x$ values for which the function is defined and included in the graph.

Given the choices, it suggests that the graph is only considering a limited range of $x$ values.

Let's analyze the options:

1. {x | –4 < x ≤ 4}
   This includes all real numbers $x$ within the interval from just greater than $-4$ to $4$. The function would be defined and graphed for all $x$ in this interval.

2. {x | –3 < x ≤ 4}
   This includes all real numbers $x$ within the interval from just greater than $-3$ to $4$.

3. {x | 1 < x ≤ 4}
   This includes all real numbers $x$ within the interval from just greater than $1$ to $4$.

4. {x | 2 < x ≤ 4}
   This includes all real numbers $x$ within the interval from just greater than $2$ to $4$.

Since the graph must show all points of the function within a given interval, the correct choice should be the interval that represents the full range where the function is graphed.

The most comprehensive range provided in the choices is:

{x | –4 < x ≤ 4}

This would include all the possible values of $x$ that could be part of the graph over that interval.

Would you like to explore more about this, or do you have any questions?

Here are some related questions:

1. How does the step size of the function $f(x) = \lceil 2x \rceil - 1$ affect the graph?
2. What would be the range of $f(x)$ if the domain were $–4 < x \leq 4$?
3. How would the graph change if the domain was $1 < x \leq 4$?
4. What is the effect of the interval $x$ on the continuity of the step function?
5. How can the function $f(x) = \lceil 2x \rceil - 1$ be defined piecewise?

Tip: When determining the domain from a graph, always consider the interval of $x$-values for which the graph exists, and ensure that all points within that interval are covered.