Questions: Which set describes the graph? x x<2 and x >= 4 x x>2 and x <= 4 x x >= 2 or x <= 4 x x<2 or x >= 4

Transcript text: Which set describes the graph? \[ \{x \mid x<2 \text { and } x \geq 4\} \] $\{x \mid x>2$ and $x \leq 4\}$ \[ \{x \mid x \geq 2 \text { or } x \leq 4\} \] $\{x \mid x<2$ or $x \geq 4\}

Solution

Solution Steps

Step 1: Analyze the graph

The graph shows a number line with a red line extending from 2 to the left indefinitely and from 4 to the right indefinitely. There is an open circle at 2, indicating that 2 is not included in the set. There is a closed circle at 4, indicating that 4 is included in the set.

Step 2: Determine the inequality for the left part

The left part of the graph represents all numbers less than 2, which can be written as $x < 2$.

Step 3: Determine the inequality for the right part

The right part of the graph represents all numbers greater than or equal to 4, which can be written as $x \geq 4$.

Step 4: Combine the inequalities

Since the graph shows two separate lines, we use the union or "or" to connect the inequalities. Thus the complete inequality is $x < 2$ or $x \geq 4$.

Step 5: Write in set builder notation

The inequality $x < 2$ or $x \geq 4$ can be written in set builder notation as $\{x \mid x < 2 \text{ or } x \geq 4\}$.