Question

worksheet 4.2
graph the set on the number line.

1. {x | x < -4 or x > 4}
2. {x | x ≥ -4} ∪ {x | x ≥ 4}

Explanation:

Step1: Identify key points for first set

For $\{x|x < - 4\text{ or }x>4\}$, key points are $x=-4$ and $x = 4$.

Step2: Graph first set

Draw an open - circle at $x=-4$ and shade to the left, draw an open - circle at $x = 4$ and shade to the right.

Step3: Identify key points for second set

For $\{x|x\geq - 4\}\cup\{x|x\geq4\}$, since $x\geq - 4$ already includes $x\geq4$, the key point is $x=-4$.

Step4: Graph second set

Draw a closed - circle at $x=-4$ and shade to the right.

Answer:

1. For $\{x|x < - 4\text{ or }x>4\}$: Open - circle at $x=-4$, shade left; open - circle at $x = 4$, shade right.
2. For $\{x|x\geq - 4\}\cup\{x|x\geq4\}$: Closed - circle at $x=-4$, shade right.