Questions: Choose the graph which corresponds to the interval x ≤ 3.

Solution Steps

To determine which graph corresponds to the interval \( x \leq 3 \), we need to identify the graph that includes all values less than or equal to 3. This means the graph should have a representation (such as a filled line or points) from the smallest value up to and including 3, and should not include any values greater than 3.

The interval given is \( x \leq 3 \). This means we are interested in all values of \( x \) that are less than or equal to 3. Mathematically, this can be expressed as the set of all \( x \) such that \( x \in [-6, 3] \).

To represent this interval on a number line, we need to mark all integers from \(-6\) to \(3\) inclusive. This can be visualized as a series of points or a continuous line segment from \(-6\) to \(3\).

The output of the graph is a list of binary values, where 1 indicates that the corresponding integer is included in the interval, and 0 indicates it is not. The list is as follows: \([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0]\).

The list corresponds to the integers from \(-6\) to \(6\). The first ten values are 1, which corresponds to the integers \(-6\) through \(3\), and the remaining values are 0, which corresponds to integers greater than 3. This matches the interval \( x \leq 3 \).

Final Answer