BACK TO TEXT

Interval Notation

An interval is part of the number line.   Interval notation is a way of writing inequalities.   Looking at the number line is a good way to do it.

Example 1.   Plot the inequality, , on the number line below.

You probably made an open circle around the 3 and made an arrow to the left, like this.

A graph using intervals would look something like this:

Notice that a right parenthesis is on the endpoint, 3 and the arrow extends to the left.  The parenthesis indicates that the ENDPOINT IS NOT INCLUDED, much like an open circle would.  

We could rewrite the inequality by picking off the interval from the number line, like this:

.  Note that the  symbol takes the place of the arrow pointing to the negative numbers indefinitely and that the parenthesis is still on the endpoint, 3.

Example 2.   Now graph the inequality  on the number line below.

If we wanted to graph the inequality  using interval notation, the graph would look like this:

We could rewrite the inequality by picking off the interval from the number line, like so:

.  Note that again the parenthesis is on the endpoint, 3,  and that the  symbol takes the place of the arrow pointing to the positive numbers indefinitely.

Now you try:

      Checkpoint Interval Notation 1

 Example 3.   Plot the inequality    on the number line below. 

You probably made open circles around the 3 and the 5 and connected them with a line segment, like this.

A graph using intervals would look like this:

As before, we can pick off the interval from the number line and write it like this:

.  Even though this might look like notation for a single point on the xy  plane, when we are discussing inequalities, it is simply another way of writing   .

Example 4.   Now, graph  .

A graph using intervals would look like this:

Notice that this time there is a bracket, ],  on the endpoint, 3.  The bracket indicates that the endpoint 3 IS INCLUDED in the graph.  The interval would look like this:  .  Notice that now there is a bracket, ], on the endpoint, 3,  but the infinity symbol still has a parenthesis.

Example 5. Plot and write as an interval:     

Now you try:

     Checkpoint Interval Notation 2

BACK TO TEXT