Question

1. $-1 \geq z$

ng graphs.

Explanation:

Step1: Analyze the inequality

The inequality is \(-1 \geq z\), which can be rewritten as \(z \leq -1\). This means we are looking for all real numbers \(z\) that are less than or equal to \(-1\).

Step2: Interpret the number line graph

On a number line, a closed circle (or filled dot) at a point indicates that the point is included in the solution set, and an open circle (or empty dot) indicates it is not. For the inequality \(z \leq -1\), we should have a closed circle at \(-1\) (since \(-1\) is included) and the arrow should point to the left (towards negative infinity) to represent all numbers less than or equal to \(-1\).

Looking at the given number line, the graph with the closed circle at \(-1\) (or the appropriate mark) and the arrow to the left would be the correct one. Wait, in the provided image, there is a graph with a closed circle (maybe at \(-4\)? Wait, no, let's re - examine. Wait, the inequality is \(-1\geq z\) or \(z\leq - 1\). So the correct graph should have a closed circle at \(-1\) and the arrow going to the left. But in the given image, there is a graph with a closed circle at \(-4\)? Wait, maybe there was a typo or mis - drawing, but assuming the intended graph for \(z\leq - 1\):

If we consider the number line, the solution to \(z\leq - 1\) is all numbers from \(-\infty\) up to and including \(-1\). So on the number line, we mark \(-1\) with a closed circle and draw an arrow to the left.

Answer:

The graph (assuming the one with the closed circle at \(-1\) - but from the given image, if we consider the left - most relevant graph, the one with the closed circle and arrow to the left starting from \(-1\) - but based on the inequality \(z\leq - 1\), the correct graphical representation is a number line with a closed circle at \(-1\) and an arrow pointing to the left.