Question

graph the interval represented in interval notation on the number line.
(-∞, 1) ∪ (10, ∞)
answer
number line:

Explanation:

Step1: Analyze the first interval \((-\infty, 1)\)

The interval \((-\infty, 1)\) means all real numbers less than \(1\). On the number line, we represent this with an open circle at \(1\) (since \(1\) is not included) and an arrow pointing to the left (towards negative infinity) from this open circle.

Step2: Analyze the second interval \((10, \infty)\)

The interval \((10, \infty)\) means all real numbers greater than \(10\). On the number line, we represent this with an open circle at \(10\) (since \(10\) is not included) and an arrow pointing to the right (towards positive infinity) from this open circle.

Step3: Combine the two intervals on the number line

We draw the number line with appropriate markings. First, mark the open circle at \(1\) and draw a line (or arrow) to the left. Then, mark the open circle at \(10\) and draw a line (or arrow) to the right. The region between \(1\) and \(10\) is not included in either interval, so we leave that part of the number line unshaded (or without the line segment).

Answer:

To graph \((-\infty, 1)\cup(10, \infty)\) on the number line:

1. At \(x = 1\), draw an open circle (since \(1\) is not in the interval) and draw a ray (line with an arrow) extending to the left (towards \(-\infty\)).
2. At \(x = 10\), draw an open circle (since \(10\) is not in the interval) and draw a ray (line with an arrow) extending to the right (towards \(\infty\)).

The number line will have two separate regions: one to the left of \(1\) (excluding \(1\)) and one to the right of \(10\) (excluding \(10\)), with the region between \(1\) and \(10\) not included in the graph.