Graphing Interval Expressions and Writing Interval Notation

This Movie (Quicktime)
will show you how to graph interval expressions and write the interval notation.

The following is the movie transcript.

Hello this is Ashley and today I am going to show you how to graph an inequality on a number line and write it in Interval Notation.

There are three rules to graphing an inequality.

First is to determine the boundaries of the inequality if they exist.

The second rule is to locate the boundaries on a number line. When the inequality is less than or greater than, the boundaries are not included. This is represented with parenthesis. You would use a closed parenthesis for less than and an open parenthesis for greater than. If the inequality is less than or equal to or greater than or equal to the boundaries are included. You would represent this with brackets. You would use a closed bracket for less than or equal to and an open bracket for greater than or equal to.

The third rule would be to shade the portion of the number line between the boundaries. If there is no boundary in one or either direction the graph continues indefinitely in that direction. In this case you would use an infinity sign.  This movie will go over how to graph these nine inequalities and write them in Interval Notation.

For our first example we will graph x is less than three. First you would start by writing a closed parenthesis over your three and shade to the left because the number of x is less than three and you would draw an arrow to indicate that it goes on infinity in that direction. To write your Interval Notation you would use an open parenthesis and it would be negative infinity and stops at three and three is not included so you use a closed parenthesis. 

Our next example we will use x is greater than negative two. Again you would start by using an open parenthesis over negative two and you would shade to the right to indicate x is greater than negative two.  For the Interval Notation you would use open parenthesis negative two and an infinity sign closed parenthesis. 

In our next example we will use x is less than or equal to two. In this example we would use a bracket because x is less than or equal to two. You would use a closed bracket to indicate two is include, and shade to the left.  The Interval Notation for this would be open parenthesis negative infinity and two and then a closed bracket to indicate two is included.

For our next example we will use x is greater than or equal to negative one. You would start by using an open bracket over negative one to indicate negative one is included and shade to the right.  And the Interval Notation for this would be open brackets negative one, infinity sign closed parenthesis. 

Our next example will be negative one is less than x and x is less than three. You would start by using an open parenthesis over negative one and a closed parenthesis over your three and x will equal everything in between.  The Interval Notation would be open parenthesis negative one and three closed parenthesis.

Our next example we will use negative one is less than or equal to x and x is less than or equal to three. In this case you would use brackets to indicate negative one and three are included and x will equal everything in between. Your Interval Notation for this would be open bracket negative one and three then closed bracket. This indicates negative one and 3 are included.

In this example one is less than x and x is less than or equal to four. So you would use an open parenthesis over your one and a closed bracket over your four and x would equal everything in between. And the Interval Notation would be open parenthesis one and four then a bracket indicating four is included.

Next we will use negative one is less than or equal to x and x is less than three. Again we will start by using a bracket for negative one and a closed parentheses for the three and x will equal everything in between. And for your Interval Notation you will use a bracket negative one and three closed parentheses.

For our last example we will use for the set of all x such that x is equal to all real numbers. This means all numbers are included. So you would shade the entire number line. The Interval Notation for this would be open parenthesis negative infinity and it goes on infinity with a closed parenthesis.

This will conclude my quick time movie on graphing inequalities and writing them in Interval Notation.

End Movie Transcript

Posted at 11:33AM Dec 05, 2006 by llinebarger in Intermediate Algebra  |