Question

graph the interval represented in interval notation on the number line.
$(-\infty, 6) \cup (11, \infty)$
answer attempt 1 out of 2
number line:
number line with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12

Explanation:

Step1: Analyze the first interval \((-\infty, 6)\)

The interval \((-\infty, 6)\) means all real numbers less than 6. On the number line, we represent this with an open circle at 6 (since 6 is not included) and an arrow pointing to the left (towards negative infinity).

Step2: Analyze the second interval \((11, \infty)\)

The interval \((11, \infty)\) means all real numbers greater than 11. On the number line, we represent this with an open circle at 11 (since 11 is not included) and an arrow pointing to the right (towards positive infinity).

Step3: Combine the two intervals (Union)

The union \((-\infty, 6) \cup (11, \infty)\) means we combine the two intervals. So we draw an open circle at 6 with a left - pointing arrow and an open circle at 11 with a right - pointing arrow on the number line.

Answer:

To graph \((-\infty, 6)\cup(11, \infty)\) on the number line:

1. For the interval \((-\infty, 6)\): Place an open circle at \(x = 6\) (because 6 is not included in the interval) and draw a line with an arrow extending to the left from the open circle (to represent all numbers less than 6).
2. For the interval \((11, \infty)\): Place an open circle at \(x=11\) (because 11 is not included in the interval) and draw a line with an arrow extending to the right from the open circle (to represent all numbers greater than 11).