How to Graph Intersections and Unions

Intersection

• 1

  Determine that an inequality represents an intersection by isolating the terms and determining whether their solution sets would cross. Using -3 < x ≤ 5 as an example, the terms create -3 < x and x ≤ 5. Note that because x can be larger than -3 while remaining smaller or equal to 5, this represents an intersection.

• 2

  Graph a compound inequality with an intersection by first creating circles on the number line at the points of each defined term. Create closed, or filled, circles if the inequality symbols for each term include an "equals to," or an open circle if it doesn't. Create an open circle on the -3 and a closed circle on the 5 for the sample inequality.

• 3

  Shade the number line to the right of terms with a "less than" sign, and to the right of terms with a "greater than" sign. Note that because this is an intersection, the shaded areas are the same area, which is the segment to the right of -3 that stops at 5.

Union

• 4

  Check the wording of the inequality to determine if it's a union, since unions are typically presented with the word "or" included. Using the inequality x < 3 or x > 9 as an example, since x cannot be less than 3 while also being greater than 9, this represents a union and not an intersection.

• 5

  Graph the left side of the inequality on the number line first. Draw a closed or open circle and shade to the appropriate side. Draw an open circle on the 3 for the sample inequality and shade to its left to represent "less than." Shade to the end of the number line and draw an arrow to represent continuation, as no end point is given for that solution set.

• 6

  Graph the right side of the inequality. Draw an open circle on the 9 and shade to its right to represent "greater than." Draw an arrow at the end of the number line to indicate continuation.