Understanding Interval Notation and Graphing Inequalities

The video tutorial explains how to graph inequalities using interval notation. It covers four cases: X > -3, X ≥ -3, X < -3, and X ≤ -3. For each case, it demonstrates how to represent the inequality on a number line using open or closed points and arrows indicating direction. The tutorial also explains how to express these intervals using interval notation, emphasizing the use of parentheses and brackets. Additionally, it provides tips on understanding inequality symbols and mentions alternative notations found in textbooks.

What type of point is used on the number line to represent that -3 is not included in the interval for X > -3?

• Arrow

• Square bracket

• Open point

• Closed point

In interval notation, how is the interval for X > -3 expressed?

• [-3, ∞)

• [-3, ∞]

• (-3, ∞]

• (-3, ∞)

For the inequality X ≥ -3, what does the closed point on -3 indicate?

• The interval is finite

• -3 is in the interval

• The interval is infinite

• -3 is not in the interval

How is the interval for X ≥ -3 written in interval notation?

• [-3, ∞)

• (-3, ∞)

• (-3, ∞]

• [-3, ∞]

What direction does the arrow point for the inequality X < -3 on the number line?

• Down

• Right

• Left

• Up

In interval notation, how is the interval for X < -3 expressed?

• (-∞, -3]

• (-∞, -3)

• [-∞, -3)

• [-∞, -3]

For the inequality X ≤ -3, what does the closed point on -3 signify?

• -3 is in the interval

• The interval is finite

• The interval is infinite

• -3 is not in the interval

How is the interval for X ≤ -3 written in interval notation?

• [-∞, -3]

• (-∞, -3)

• (-∞, -3]

• [-∞, -3)

What is the relationship between the inequality symbol and the direction of the arrow on the number line?

• They are perpendicular

• They are unrelated

• They point in the same direction

• They point in opposite directions

What alternative notation might you see in textbooks instead of open and closed points?

• Arrows

• Dashes

• Stars

• Rounded parenthesis and square brackets