Set Representation in Interval Notation and Number Line Graphing
The image shows a worksheet asking to write the set in interval notation and to graph it on a number line. The set given is {x | x ≤ -1/2 or x > 3/2}.
For interval notation, this set is a union of two intervals:
- The first part, "x ≤ -1/2", is an interval that includes all numbers to the left of and including -1/2. In interval notation, this is written as (-∞, -1/2], using a square bracket to indicate that -1/2 is included in the set.
- The second part, "x > 3/2", is an interval that includes all numbers strictly greater than 3/2. This does not include the endpoint 3/2, so we use a parenthesis. In interval notation, this is written as (3/2, ∞).
The complete interval notation for the set is the union of these two intervals:
(-∞, -1/2] ∪ (3/2, ∞).
On the number line:
a) Shade all points to the left of and including -1/2.
b) Shade all points strictly to the right of 3/2.
We use a closed dot or a bracket on -1/2 to show that -1/2 is included, and an open dot or a parenthesis just to the right of 3/2 to show that the interval starts after 3/2 and continues indefinitely to the right.
