How do you graph a set on a number line and express it in interval notation?

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Graphing a Set on the Number Line

Graphing a set on a number line is a straightforward process. To illustrate this, let’s assume our set is S = {x | -3 < x < 2}. Here’s how you can effectively graph this set:

  1. Draw a Horizontal Line: Begin by drawing a straight horizontal line, which will represent your number line.
  2. Mark the Relevant Points: Identify the key numbers from your set. In our case, these are -3 and 2. Put a small circle or dot on these numbers to indicate that they are not included in the set, because we have greater than and less than signs.
  3. Shade the Region: Shade the line between -3 and 2. This shading represents that all numbers between these two points are included in the set.

Expressing the Set in Interval Notation

Now, let’s convert our set into interval notation. This is a concise way to express the entire set of real numbers that fall within our specified range.

For our example of S = {x | -3 < x < 2}, the interval notation would be:

        (-3, 2)

This notation indicates that the set includes all numbers greater than -3 and less than 2, but does not include -3 and 2 themselves.

Conclusion

To summarize, first draw the number line, mark and denote the endpoints, and then shade the region representing the numbers in your set. Finally, use interval notation to succinctly describe this range.

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