Question

What interval notation represents the data graphed below?

A. [-∞, -2) U [4, ∞]
B. [-∞, -2] U (4, ∞]
C. (-∞, -2] U (4, ∞]
D. (-∞, -2) U [4, ∞)

Answer 1

Answer: Choice D

`(-\infty, -2) \cup [4, \infty)`

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Step-by-step explanation:

The left portion is the interval (-∞, -2)

This is a shorthand way of saying
`-\infty < x < -2`

The curved parenthesis says "do not include this endpoint as part of the solution set". Note the open hole at x = -2 in the diagram.

In contrast, the value x = 4 is included (due to the filled in circle), so we use a square bracket for this endpoint. Therefore, the right-hand portion is represented by [4, ∞) which translates to
`4 \le x < \infty`

Negative and positive infinity will always use a parenthesis, and never a square bracket. This is because we can only approach infinity but never reach it, so we cannot include it as an endpoint.

All of this builds up to the full interval notation to be
`(-\infty, -2) \cup [4, \infty)`

The only square bracket is near the 4; everything else is a curved parenthesis. This is why choice D is the final answer.