Questions: Which set describes the graph? x x ≤ -1 and x > 0 x x ≤ -1 or x > 0 x x < -1 or x ≥ 0 x x < -1 and x ≥ 0

Transcript text: Which set describes the graph? \[ \{x \mid x \leq-1 \text { and } x>0\} \] \[ \{x \mid x \leq-1 \text { or } x>0\} \] \[ \{x \mid x<-1 \text { or } x \geq 0\} \] \[ \{x \mid x<-1 \text { and } x \geq 0\} \]

Solution

Solution Steps

Step 1: Analyze the graph

The graph shows two rays. One ray starts at -1 and extends to the left. The other ray starts at 0 and extends to the right. There is a hollow circle at -1, indicating that -1 is not included in the solution. There is a solid circle at 0, indicating that 0 is included in the solution.

Step 2: Describe the rays with inequalities

The ray extending to the left from -1 represents the inequality _x_ < -1.

The ray extending to the right from 0 represents the inequality _x_ ≥ 0.

Step 3: Combine the inequalities

Since the graph displays two separate rays, the solution is the union of the two inequalities. We use "or" to represent the union.