Understanding Intervals: Inequality, Graph, and Interval Notation

This video tutorial covers how to express intervals using inequality notation, graphing, and interval notation. It begins with basic examples, demonstrating how to graph intervals and express them in different notations. The tutorial progresses to more complex examples, including absolute value inequalities and compound inequalities. The video emphasizes understanding the use of open and closed intervals, union of intervals, and the concept of infinity in interval notation.

What is the correct interval notation for the inequality X < 5 or X ≥ -1?

• (-∞, 5) ∪ [-1, 5]

• (-∞, 5] ∪ [-1, ∞)

• (-∞, 5) ∪ (-1, ∞)

• (-∞, 5) ∪ [-1, ∞)

How is the inequality |x| ≥ 2 expressed in terms of two separate inequalities?

• X > 2 or X < -2

• X ≤ 2 or X ≥ -2

• X ≥ 2 or X ≤ -2

• X > 2 and X < -2

What is the interval notation for the inequality X ≥ 2 or X ≤ -2?

• [-2, ∞) ∪ (-∞, 2]

• (-∞, -2) ∪ (2, ∞)

• (-∞, -2] ∪ [2, ∞)

• (-2, ∞) ∪ (-∞, 2)

Which of the following represents the interval (-∞, -6] ∪ [-4, ∞) in inequality notation?

• X < -6 and X > -4

• X ≤ -6 and X ≥ -4

• X ≤ -6 or X ≥ -4

• X < -6 or X > -4

What is the correct graph representation for the interval (-∞, 4) ∪ (4, ∞)?

• Open point at 4 with arrows extending left and right

• Closed point at 4 with arrows extending left and right

• Open point at 4 with arrows extending only to the right

• Closed point at 4 with arrows extending only to the left

How would you express the interval (-∞, 4) ∪ (4, ∞) using inequalities?

• X ≤ 4 or X ≥ 4

• X < 4 and X > 4

• X < 4 or X > 4

• X ≤ 4 and X ≥ 4

In the graph with an open point on -1 and a closed point on 0, what is the inequality notation?

• X ≤ -1 or X > 0

• X < -1 and X ≥ 0

• X < -1 or X ≥ 0

• X ≤ -1 and X > 0

What is the interval notation for a graph with an open point on -2 and an open point on 1?

• (-∞, -2) ∪ (1, ∞)

• (-∞, -2) ∪ (-1, 1)

• (-∞, -2) ∪ (-1, 1)

• (-∞, -2) ∪ (1, ∞)

Which of the following represents the compound inequality X > -1 and X < 1?

• (-1, 1]

• (-1, 1)

• [-1, 1)

• [-1, 1]

How do you express the interval from -1 to 1, excluding both endpoints, in interval notation?

• [-1, 1]

• [-1, 1)

• (-1, 1)

• (-1, 1]