Question

which compound inequality could be represented by the graph?
-5 -4 -3 -2 -1 0 1 2 3 4 5
○ $-4 \leq x \leq 4$
○ $-2 \leq x \leq -1$
○ $x \leq -1$ or $x \geq 0$
○ $x \leq 3$ or $x \geq -1$

Explanation:

Step1: Analyze the graph's direction

The graph has two arrows: one going to the left from -1 (including -1) and one going to the right from 0 (including 0). So we need a compound inequality with "or" that includes \( x \leq -1 \) and \( x \geq 0 \).

Step2: Check each option

• Option 1: \(-4 \leq x \leq 4\) is a single interval between -4 and 4, not matching the two - part graph.
• Option 2: \(-2 \leq x \leq -1\) is a single interval between -2 and -1, not matching.
• Option 3: \( x \leq -1 \) or \( x \geq 0 \) matches the two - part graph (left from -1, right from 0).
• Option 4: \( x \leq 3 \) or \( x \geq -1 \) would cover almost the entire number line (since -1 to 3 is included in both, and outside is also included), not matching the graph.

Answer:

C. \( x \leq -1 \) or \( x \geq 0 \)